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From Financial Stability to Digital Payments: Empirical Insights into Central Banking
Full text linkThe new millennium has been characterized by rising digitalization, the proliferation of shadow banking, and significant advancements in machine learning and natural language processing. These trends present both challenges and opportunities, which my dissertation addresses. This cumulative dissertation investigates critical aspects of financial stability, monetary policy, and the transition towards cashless economies through three distinct but interrelated studies.
The first paper examines the risk-taking channel of monetary policy transmission within the euro area, focusing on shadow banks. Through vector autoregressive models, it assesses the impact of conventional and unconventional monetary policy shocks on shadow banks' asset growth and risk asset ratios. The results indicate that lower interest rates lead to a portfolio reallocation towards riskier assets and a general expansion of assets in shadow banks. In the case of conventional monetary policy shocks, both effects last three times as long as in the case of unconventional monetary policy shocks. Country-specific as well as sector-specific estimations confirm these findings. This study bridges gaps in the existing literature, especially in the eurozone, by highlighting the significant role shadow banks play in monetary policy transmission, suggesting implications for financial regulation and stability.
The second paper explores the influence of financial stability considerations on US monetary policy, particularly during the Great Recession. Utilizing natural language processing and machine learning techniques on congressional hearings, this study constructs indicators for financial stability sentiment expressed by the Federal Reserve Chairs. Empirical analysis is conducted using Taylor-rule models, revealing that negative financial stability sentiment is associated with a more accommodative monetary policy stance, even before the Great Recession. This work provides new insights into the integration of financial stability concerns into monetary policy frameworks, demonstrating the need for a balanced approach to economic stability. The article suggests that under a dual mandate, such as that of the Federal Reserve, financial stability can, to some extent, already be factored into monetary policy deliberations.
The third paper sheds new light on ``cash paradox'' by uncovering the factors of the cashless transition that has not been entirely understood so far. Using a comprehensive dataset across 65 countries, the study employs panel data models to explain the paradox (increasing demand for central bank money despite soaring digitalization), especially among technologically advanced countries, e.g., Japan. Empirical evidence suggests that digitalization is not significantly associated with higher reliance on physical cash. It uncovers a unique non-linear relationship between trust and cash usage (``Arch of Trust'') which holds after addressing potential endogeneity issues using 2SLS estimation. Opposed to the widespread misinterpretations of Keynes' (1937) reasons for holding cash, the findings highlight that distrust is the key factor unlocking two distinct puzzles in economics, linking cash hoarding with ``missing'' funds on capital markets and slower shift toward digital payments in low-trust societies. A key insight is the role of trust as a (social) insurance, cushion or safety net, dampening the perception of risk and reducing precautionary and transactionary demand for physical cash, while encouraging a shift towards riskier alternatives. This, in turn, is connected to the third puzzle, the ``paradox of prudence.'' A shift from riskier investments to safer assets, cash, may be prudent at the individual level but risky for the overall economy, a concern for macroprudential policymakers. Additionally, the research highlights the critical role of culture in driving the global movement towards cashless economies. Moreover, cultures that are more self-expression-oriented (which is the main cultural dimension) and culturally closer to Sweden are associated with less cash-intensive economies. These insights are vital for macroprudential regulators as well as for policymakers designing payment systems and CBDC in culturally diverse regions like the Eurozone.
Collectively, these papers contribute to a deeper understanding of monetary policy, financial stability, and the transition from cash-based to (nearly) cashless societies, offering significant theoretical and practical implications for academics, regulators and central bankers
Variable Stress Patterns in English Complex Adjectives: Inter-Individual Differences and the Nature of the Morphology-Phonology Interface
Full text linkThe present dissertation deals with variable stress patterns in English complex adjectives such as celebratory, identifiable or imaginative. This variation is usually described in terms of retaining the stress from the embedded base (idéntify -> idéntifiable) or deviating from the stress of the embedded base (idéntify -> identifíable). While several accounts have explored this variation, none of them have been able to identify a plausible reason for why it occurs. Additionally, the role of individual speaker differences has been disregarded in the discussion. This dissertation therefore explores the empirically observable extent of the variation and investigates possible causes of it with a special focus on individual differences between speakers. It uses data from a complex online experiment that included five different tasks to assess speakers' stress production, perception, morphological processing, vocabulary size and other factors. It furthermore tests the predictions of previous accounts on the large set of authentic utterances from speakers collected using this online experiment. The data show that individual differences in vocabulary size between speakers are a significant predictor of a speaker's tendency to retain the stress of the embedded base
Building on Social Virtual Reality to Support Flexible Collaboration and Enrich Therapy Sessions
Full text linkSocial virtual environments allow their users to meet and collaborate in a shared three-dimensional space, even when far apart from each other in the real world. Within these spaces, the appearance and interaction capabilities of both users and environments can be adapted and changed in a myriad of ways. To enable virtual environments to fulfill their potential of supporting a wide variety of collaboration use-cases, both the impacts of basic interaction design decisions and the individual needs of specific usage areas need to be explored further.
This thesis approaches this topic in two ways. First, the basic building blocks of collaboration in social virtual environments are explored by asking the question: "How can social virtual spaces that allow interaction beyond real-world constraints utilize the potential of mutual assistance and shared workflows between multiple users?". Going into further detail for a serious use-case in which direct collaborative interactions and their effect on the included users are especially important, it then explores the potential of collaborative virtual spaces in the therapy domain by asking "How can the potential of social virtual spaces be utilized to support and improve therapy encounters?"
With regards to the first research question, the thesis presents two theoretical frameworks detailing different aspects of supporting smooth and varied collaboration processes. In addition, several user studies on the topic of collaborative virtual interaction are described, focusing on the role that different users can play during shared interaction and the effects that this distribution of roles and responsibilities has on both the performance and experience of the involved user pairs.
The results presented for this first research question show that social virtual spaces have the potential to provide dedicated support for collaborative workflows. To enable users to adapt their working mode individually and as a team, interaction techniques should complement a team's natural interaction and communication. When presenting novel interactions to users, providing them with a way to support each other can ease their adaptation to these interactions. In these cases, the inclusion of all interested collaborators as active participators should be prioritized in order to let all users benefit from being immersed in a virtual environment.
Addressing the combination of social virtual spaces with therapy in relation to the second research question, this thesis presents the result of a series of interviews with practicing physio- and psychotherapists. Motivated by the recorded expert feedback, it also reports on two more detailed explorations of specific areas of interest. The work presented for the second research question demonstrated the promise of using virtual environments in both exercise- and conversation-based therapy practice. Investigating the potential of shared interactions, the exploration of virtual recordings and the adaptation of virtual appearances, the presented work uncovered several topic areas that could be further explored regarding their possible use in the treatment of patients.
Taken together, the six research articles presented in this thesis show both the value of supporting and understanding shared interactions in virtual spaces and their potential place in serious use-cases like the therapy domain. When introducing shared virtual environments to new user groups, the opportunity for mutual support through shared interaction techniques could be a crucial building block towards making virtual spaces both accessible and attractive to a variety of users.Soziale virtuelle Räume bieten ihren Nutzenden die Möglichkeit, sich in einer gemeinsamen Umgebung zu treffen und dort zusammenzuarbeiten, selbst wenn sie in der realen Welt weit voneinander entfernt sind. In diesen geteilten Räumen ist es möglich, das Aussehen und die Interaktionsfähigkeit der Nutzenden und der Umgebung auf vielfältige Art anzupassen und zu verändern.
Dies verleiht virtuellen Umgebungen das Potential, viele verschiedene Kollaborationsprozesse zu unterstützen. Jedoch müssen dafür sowohl die Auswirkungen grundlegender Designentscheidungen als auch die individuellen Anforderungen verschiedener Einsatzbereiche gezielt untersucht werden.
Diese Arbeit nähert sich dieser Herausforderung auf zwei verschiedene Arten. Zunächst werden grundlegende Aspekte der Kollaboration in virtuellen Umgebungen durch die Fragestellung: "Wie können soziale virtuelle Umgebungen, die über die Möglichkeiten der realen Welt hinaus gehen, das Potenzial von gegenseitiger Unterstützung und geteilten Arbeitsabläufen zwischen mehreren Nutzenden ausschöpfen?" untersucht. Danach wird mit der Fragestellung "Wie kann das potential sozialer virtueller Räume genutzt werden, um Therapie-Begegnungen zu unterstützen und zu verbessern?" ein Themenfeld näher beleuchtet, in dem die direkte kollaborative Interaktion und deren Auswirkung auf ihre Nutzenden einen besonderen Stellwert hat.
Hinsichtlich der ersten Forschungsfrage präsentiert die Arbeit zwei theoretische Frameworks, die verschiedene Aspekte der Unterstützung von reibungslosen und abwechslungsreichen Kollaborationsprozessen beleuchten. Zudem werden mehrere Benutzungsstudien zum Thema der kollaborativen virtuellen Interaktion beschrieben. Dies geschieht unter besonderer Betrachtung der verschiedenen Rollen, die Nutzende bei der gemeinsamen Interaktion spielen können und der Effekte, welche die Verteilung dieser Rollen und Verantwortungsbereiche auf die Leistung und Erfahrungen der einzelnen Nutzenden hat.
Die Ergebnisse, die in diesem Teil der Arbeit vorgestellt werden, zeigen, dass soziale virtuelle Umgebungen das Potenzial haben kollaborative Arbeitsprozesse zu unterstützen. Insbesondere sollte es Nutzenden von virtuellen Umgebungen ermöglicht werden, ihre Arbeitsweise im virtuellen Raum an ihre individuellen und gemeinsamen Bedürfnisse anzupassen. Um dies zu erreichen, sollten die angebotenen Interaktionstechniken die natürliche Interaktion und Kommunikation der Teams komplementieren. Wenn Nutzende mit neuen Interaktionstechniken konfrontiert werden, kann es zudem helfen ihnen die Möglichkeit zu geben sich gegenseitig zu unterstützen. In diesen Fällen sollte die Einbeziehung von allen interessierten Kollaborierenden als aktive Teammitglieder priorisiert werden damit möglichst viele von ihnen von der Immersion in die virtuelle Umgebung profitieren.
Mit Blick auf die zweite Forschungsfrage zum Einsatz von sozialer virtueller Realität in der Therapie präsentiert die Arbeit die Ergebnisse einer Interview-Reihe mit praktizierenden Therapeutinnen und Therapeuten und, motiviert durch dieses Expertenfeedback, zwei Studien zu den spezifischeren Themen der Selbstdarstellung und der Erkundung von aufgezeichneten Nutzerdaten im virtuellen Raum. Die Ergebnisse der zweiten Forschungsfrage konnten zeigen, dass virtuelle Umgebungen vielfältige Möglichkeiten für die Therapie-Praxis bieten. Zudem wurden mehrere Themenfelder aufgezeigt, die weiter hinsichtlich ihres Potenzials für die Patientenbehandlung untersucht werden könnten. Weitere diesbezügliche Arbeiten sollten auf gemeinsamen Design und Evaluationsprozessen von praktizierenden Therapeuten und VR-Forschenden aufbauen.
Zusammengenommen zeigen die Ergebnisse dieser Arbeit sowohl den Wert davon Kollaborationsprozesse in virtuellen Räumen zu verstehen und unterstützen, als auch das Potential, welches sie für wichtige Anwendungsfelder wie die Therapie bieten. Wenn Nutzergruppen an neue virtuelle Umgebungen herangeführt werden, könnte die Ermöglichung gegenseitiger Unterstützung durch geteilte Interaktionstechniken einen fundamentalen Anteil daran haben, diese für eine weite Spannbreite an Nutzenden und Anwendungsfeldern zugänglich und attraktiv zu machen
A Framework for Multiobjective and Uncertain Resource Allocation Problems in Survey Sampling based on Conic Optimization
Full text linkIn most textbooks optimal sample allocation is tailored to rather theoretical examples. However, in practice we often face large-scale surveys with conflicting objectives and many restrictions on the quality and cost at population and subpopulation levels. This multiobjectiveness results in a multitude of efficient sample allocations, each giving different weight to a single survey purpose. Additionally, since the input data to the allocation problem often relies on supplementary information derived from estimation, historical data, or expert knowledge, allocations might be inefficient when specified for sampling.
This doctoral thesis presents a framework for optimal allocation to standard sampling schemes that allows for specifying the tradeoff between different objectives and analyzing their sensitivity to other problem components, aiming to support a decision-maker in identifying an at-most preferred sample allocation. It dedicates a full chapter to each of the following core questions: 1) How to efficiently incorporate quality and cost constraints for large-scale surveys, say, for thousands of strata with hundreds of precision and cost constraints? 2) How to handle vector-valued objectives with their components addressing different, possibly conflicting survey purposes? 3) How to consider uncertainty in the input data?
The techniques presented can be used separately or in combination as a general problem-solving framework for constrained multivariate and multidomain, possibly uncertain, sample allocation. The main problem is formulated in a way that highlights the different components of optimal sample allocation and can be taken as a gateway to develop solution strategies to each of the questions above, while shifting the focus between different problem aspects. The first question is addressed through a conic quadratic reformulation, which can be efficiently solved for large problem instances using interior-point methods. Based on this the second question is tackled using a weighted Chebyshev minimization, which provides insight into the sensitivity of the problem and enables a stepwise procedure for considering nonlinear decision functionals. Lastly, uncertainty in the input data is addressed through regularization, chance constraints and robust problem formulations
Wohnen in Rheinland-Pfalz. Herausforderungen für eine soziale Wohnungspolitik
Full text linkDiese Studie untersucht die aktuelle Situation auf dem Wohnungsmarkt und die Wohnungspolitik in Rheinland-Pfalz. Sie zeigt, dass in den Städten hohe Mieten und Immobilienpreise, geringe Wohnflächen und eine starke Mietbelastung insbesondere einkommensschwacher Haushalte dominieren. Etwas anders gelagert stellt sich die Lange in den ländlichen Regionen dar: Zwar spielt Eigentum hier eine größere Rolle und der Wohnungsmarkt ist insgesamt entspannter, jedoch schränkt der kleine Mietwohnungsmarkt die Möglichkeiten für Haushalte mit geringem Einkommen erheblich ein. Zudem breiten sich Preissteigerungen zunehmend aus den Städten in umliegende ländliche Räume aus, insbesondere im Umland von Mainz, entlang des Rheins und im Umfeld von Luxemburg.
Die in Rheinland-Pfalz angewandten wohnungspolitischen Instrumente – von Mietspiegel und Mietpreisbremse bis zur sozialen Wohnraumförderung – haben nur einen dämpfenden Effekt auf die Wohnungsmarktentwicklung, beheben aber nicht die strukturellen Ursachen der Wohnungsfrage. Insbesondere der Rückgriff auf private Investor:innen und zeitlich befristete Sozialbindungen erweisen sich als grundlegende Konstruktionsfehler. Für eine zukunftsfähige soziale Wohnungspolitik müssen Strukturen gefördert werden, die jenseits des Marktmechanismus agieren. Nur so kann eine verlässliche soziale Wohnraumversorgung umgesetzt werden
Unveiling Extracellular Enzyme Activities in Aquatic Biofilms by Innovative Methodological Approaches for Ecological Research
Full text linkExtracellular enzymes in microbial communities play a central role in nutrient cycling and the degradation of (pollutant) substances in various natural and anthropogenic systems. Bound in aquatic biofilms, sludge aggregates, or even unbound at their interfaces, they are of great importance for both the environment and human health. In particular, in wastewater treatment plants and inland waters, hydrolytic activities influence the wide-reaching efficiency of nutrient removal and self-purification, thus contributing significantly to overall water quality.
The main goal of this dissertation project was to investigate the factors that influence enzymatic activity and the health of microbial communities in activated sludge and river systems, particularly in relation to anthropogenic influences and natural environmental conditions. The aim was to contribute to a better understanding of the sensitivity of our freshwater ecosystems and to support the long-term preservation of water quality and ecological stability. The development and optimization of appropriate methods, as well as their testing and applicability, were the focal points.
For this purpose, a fluorometric microplate assay was developed and adapted to determine both extracellular enzyme activities (EEAs) in activated sludge samples and in intact biofilms. Its suitability for field studies was subsequently tested. Inhibition and activity of selected hydrolases under different conditions were investigated to better understand the mechanisms and potential environmental risks posed by anthropogenic influences and seasonal fluctuations of hydrochemical and climatic parameters.
The first phase of the doctoral thesis involved studies on the inhibition of alkaline phosphatase in activated sludge by oxyanions. Using the fluorometric microplate assay, the inhibitory effect was sensitively detected over a pH range of 7.0 to 8.5. IC50- and IC20-concentrations were calculated from modeled dose-response functions. It was found that vanadate and tungstate caused strong inhibitory effects, while molybdate moderately inhibited the enzyme. An increasing pH led to a reduction in the inhibitory effect of tungstate and molybdate. The inhibition effects of vanadate were not significantly affected by the pH. In municipal wastewater, the concentrations of such metal ions are usually low, but industrial wastewater may have pollutant loads that can significantly impact the removal of phosphorus-containing compounds, and thus the efficiency of treatment plants.
In the second phase, an attempt was made to further adapt the developed methodology to investigate EEA and kinetics in intact freshwater biofilms. Four different types of bead materials (lava, glass, sintered quartz, and ceramics) fitting into a 96-well microplate were tested as carriers for biofilms on both the laboratory and field scale. The analysis included a total of seven hydrolases as representatives of key nutrient cycles such as phosphorus, carbon, and nitrogen: phosphatases, glucosidases, peptidases (two different types), and sulfatase. Experiments with increasing substrate concentrations led to classical kinetic profiles according to the Michaelis-Menten mechanism. This allowed for the prediction of the biofilm enzymes’ response to different substrate concentrations. Parameters such as Vmax and Km could be derived from the modeled curves.
Ceramic beads are particularly suitable for long-term studies due to their high stability, while sintered quartz beads should be preferred for the use in stagnant media (material loss under turbulent conditions). Lava and glass beads, on the other and, proved suboptimal for uniform biofilm development due to their surface properties. The potential use of this fast and sensitive test for ecotoxicological or even human-toxicological studies was demonstrated by the effects of caffeine on the activity of PDE. The result of this part of the research represents a powerful tool for assessing environmental pollution and monitoring water quality.
The high application potential was clearly highlighted in the final phase of the project. The goal here was to deepen the understanding of interactions between seasonal factors, anthropogenic influences, and biofilm processes in rivers by investigating EEA and biofilm parameters such as biomass and relating them to hydrochemical and climatic factors. Ceramic beads were exposed both upstream and downstream of a wastewater treatment plant discharge and sampled over a period of seven months. EEAs and biomass varied depending on the season and location, with higher microbial activity observed upstream in winter. Winter conditions led to the dilution of most nutrients as well as in an increse of dissolved oxygen. Nutrient concentrations analyzed downstream were significantly higher in the summer. Accumulation of nutrient or pollutants during the summer months cannot be excluded, which may have led to a general reduction in enzyme activities.
Potential causes could be inhibitory effects on the enzymes, or a reduced enzyme activity due to a sufficiently high nutrient supply. In general, the sampling site upstream showed a more pronounced seasonal dynamics, with a significant proportion of the variance in biological parameters (activity and biomass) attributable to seasonal factors. A secondary component, likely reflecting the impact of the treatment plant discharge, explained another portion of the data variance. Regardless of the season, high correlations between biological parameters were observed upstream, while downstream the data were more decorrelated. This could be because the biofilms, under chronic stress, respond less dynamically to seasonal fluctuations.
This dissertation illustrates that in addition to anthropogenic stress factors, seasonal fluctuations of hydrochemical and climatic parameters should also be considered in "stress downstream the pipe" studies. The selected methods are recommended for explaining and considering the data variance, as they highlight the complex interplay between microbial enzymatic activity, environmental factors, and pollutants in the activated sludge of wastewater treatment plants and also in aquatic systems. The novel bead assay could pave the way for the future standardization of effect-oriented studies on intact aquatic biofilms
Shape Optimization Constrained by Nonlocal Equations
Full text linkPartial differential equations are not always suited to model all physical phenomena, especially, if long-range interactions are involved or if the actual solution might not satisfy the regularity requirements associated with the partial differential equation. One remedy to this problem are nonlocal operators, which typically consist of integrals that incorporate interactions between two separated points in space and the corresponding solutions to nonlocal equations have to satisfy less regularity conditions.
In PDE-constrained shape optimization the goal is to minimize or maximize an objective functional that is dependent on the shape of a certain domain and on the solution to a partial differential equation, which is usually also influenced by the shape of this domain. Moreover, parameters associated with the nonlocal model are oftentimes domain dependent and thus it is a natural next step to now consider shape optimization problems that are governed by nonlocal equations.
Therefore, an interface identification problem constrained by nonlocal equations is thoroughly investigated in this thesis. Here, we focus on rigorously developing the first and second shape derivative of the associated reduced functional. In addition, we study first- and second-order shape optimization algorithms in multiple numerical experiments.
Moreover, we also propose Schwarz methods for nonlocal Dirichlet problems as well as regularized nonlocal Neumann problems. Particularly, we investigate the convergence of the multiplicative Schwarz approach and we conduct a number of numerical experiments, which illustrate various aspects of the Schwarz method applied to nonlocal equations.
Since applying the finite element method to solve nonlocal problems numerically can be quite costly, Local-to-Nonlocal couplings emerged, which combine the accuracy of nonlocal models on one part of the domain with the fast computation of partial differential equations on the remaining area. Therefore, we also examine the interface identification problem governed by an energy-based Local-to-Nonlocal coupling, which can be numerically computed by making use of the Schwarz method. Here, we again present a formula for the shape derivative of the associated reduced functional and investigate a gradient based shape optimization method.Partielle Differentialgleichungen sind nicht immer zur Modellierung mancher physikalischer Phänomene geeignet, insbesondere wenn Interaktionen über größere Distanzen involviert sind oder die eigentliche Lösung eventuell nicht die Regularitätsbedingungen der partiellen Differentialgleichung erfüllt. Die Antwort hierzu kann die Verwendung von nichtlokalen Operatoren sein, welche typischerweise aus Integraloperatoren bestehen, die die wechselseitige Beziehung zweier unterschiedlicher Punkte im Raum berücksichtigen. Zudem sind die Reguläritätsanforderungen an die Lösung eines dazugehörigen nichtlokalen Problems meist geringer.
In der durch partielle Differentialgleichungen beschränkten Formoptimierung versucht man den Wert eines Zielfunktionals, welches abhängig ist von der Form eines bestimmten Gebietes und von der Lösung einer ebenfalls von der Form abhängigen partiellen Differentialgleichung, zu minimieren oder zu maximieren. Da zudem oft nichtlokale Probleme betrachtet werden, bei denen Parameter ebenfalls vom der Form des Gebietes beeinflusst werden, ist es ein logischer nächster Schritt, Formoptimierungsprobleme zu untersuchen, die abhängig von der Lösung eines solchen Form-abhängigen nichtlokalen Problems sind. Aus den angeführten Gründen wird in dieser Arbeit das Problem der Identifizierung eines Interfaces unter Berücksichtigung eines Interface-abhängigen nichtlokales Problems detailliert untersucht. Hierbei liegt der Fokus auf der präzisen Herleitung der ersten und zweiten Formableitung des reduzierten Zielfunktionals. Zusätzlich werden Algorithmen erster und zweiter Ordnung zur Formoptimierung in einer Vielzahl an numerischen Experimenten untersucht.
Darüber hinaus werden Schwarz Methoden zum Lösen von nichtlokalen Dirichlet Problemen sowie regularisierter nichtlokaler Neumann Problemen eingeführt. Insbesondere wird die Konvergenz des multiplikativen Schwarz-Ansatzes bewiesen. Darüber hinaus werden verschiedene Eigenschaften der Schwarz Methode für nichtlokale Probleme in numerischen Untersuchungen veranschaulicht.
Da die Anwendung der Methode der finiten Elemente zur numerischen Lösung von nichtlokalen Problemen rechenintensiv sein kann, sind Lokal-zu-Nichtlokalen Kopplungen entwickelt worden, die die Genauigkeit der nichtlokalen Modelle auf einem Teilbereich mit der schnellen Lösbarkeit der partiellen Differentialgleichung auf dem verbliebenen Teil des Gebietes verknüpfen. Aufgrund dessen wird das Problem der Interface-Identifizierung unter Berücksichtigung einer Energie-basierten Lokal-zu-Nichtlokaler Kopplung untersucht. Hierbei lässt sich die Lokal-zu-Nichtlokale Kopplung durch die Schwarz Methode numerisch lösen. Darüber hinaus wird ebenfalls eine Formel für die erste Formableitung des reduzierten Zielfunktionals vorgestellt und zudem wird ein Gradienten-basierter Formoptimierungsalgorithmus getestet
Uniqueness Results and Universality of Fourier Series in Dirichlet-type Spaces
Full text linkAlthough universality has fascinated over the last decades, there are still numerous open questions in this field that require further investigation. In this work, we will mainly focus on classes of functions whose Fourier series are universal in the sense that they allow us to approximate uniformly any continuous function defined on a suitable subset of the unit circle.
The structure of this thesis is as follows. In the first chapter, we will initially introduce the most important notation which is needed for our following discussion. Subsequently, after recalling the notion of universality in a general context, we will revisit significant results concerning universality of Taylor series. The focus here is particularly on universality with respect to uniform convergence and convergence in measure. By a result of Menshov, we will transition to universality of Fourier series which is the central object of study in this work.
In the second chapter, we recall spaces of holomorphic functions which are characterized by the growth of their coefficients. In this context, we will derive a relationship to functions on the unit circle via an application of the Fourier transform.
In the second part of the chapter, our attention is devoted to the spaces which can be viewed as the set of harmonic functions contained in the W^{1,p}(\D) Sobolev spaces. In this context, we will also recall the Bergman projection. Thanks to the intensive study of the latter in relation to Sobolev spaces, we can derive a decomposition of spaces which may be seen as analogous to the Riesz projection for spaces. Owing to this result, we are able to provide a link between spaces and spaces of holomorphic functions on \mathbb{C}_\infty \setminus \s which turns out to be a crucial step in determining the dual of spaces.
The last section of this chapter deals with the Cauchy dual which has a close connection to the Fantappié transform. As an application, we will determine the Cauchy dual of the spaces and , two results that will prove to be very helpful later on. Finally, we will provide a useful criterion that establishes a connection between the density of a set in the direct sum and the Cauchy dual of the intersection of the respective spaces.
The subsequent chapter will delve into the theory of capacities and, consequently, potential theory which will prove to be essential in formulating our universality results. In addition to introducing further necessary terminologies, we will define capacities in the first section following [16], however in the frame of separable metric spaces, and revisit the most important results about them.
Simultaneously, we make preparations that allow us to define the -capacity which will turn out to be equivalent to the classical Riesz -capacity. The -capacity proves to be more adapted to the spaces. It becomes apparent in the course of our discussion that the -capacity is essential to prove uniqueness results for the class . This leads to the centerpiece of this chapter which forms the energy formula for the -capacity on the unit circle. More precisely, this identity establishes a connection between the energy of a measure and its corresponding Fourier coefficients. We will briefly deal with the complement-equivalence of capacities before we revisit the concept of Bessel and Riesz capacities, this time, however, in a much more general context, where we will mainly rely on [1]. Since we defined capacities on separable metric spaces in the first section, we can draw a connection between Bessel capacities and -capacities. To conclude this chapter, we would like to take a closer look at the geometric meaning of capacities. Here, we will point out a connection between the Hausdorff dimension and the polarity of a set, and transfer it to the -capacity. Another aspect will be the comparison of Bessel capacities across different dimensions, in which the theory of Wolff potentials crystallizes as a crucial auxiliary tool.
In the fourth chapter of this thesis, we will turn our focus to the theory of sets of uniqueness, a subject within the broader field of harmonic analysis. This theory has a close relationship with sets of universality, a connection that will be further elucidated in the upcoming chapter.
The initial section of this chapter will be dedicated to the notion of sets of uniqueness that is specifically adapted to our current context. Building on this concept, we will recall some of the fundamental results of this theory.
In the subsequent section, we will primarily rely on techniques from previous chapters to determine the closed sets of uniqueness for the class . The proofs we will discuss are largely influenced by [16, p.\ 178] and [9, pp.\ 82].
One more time, it will become evident that the introduction of the -capacity in the third chapter and the closely associated energy formula on the unit circle, were the pivotal factors that enabled us to carry out these proofs.
In the final chapter of our discourse, we will present our results on universality. To begin, we will recall a version of the universality criterion which traces back to the work of Grosse-Erdmann (see [26]). Coupled with an outcome from the second chapter, we will prove a result that allows us to obtain the universality of a class using the technique of simultaneous approximation. This tool will play a key role in the proof of our universality results which will follow hereafter.
Our attention will first be directed toward the class with in the interval . Here, we summarize that universality with respect to uniform convergence occurs on closed and -polar sets E \subset \s. Thanks to results of Carleson and further considerations, which particularly rely on the favorable behavior of the -kernel, we also find that this result is sharp. In particular, it may be seen as a generalization of the universality result for the harmonic Dirichlet space.
Following this, we will investigate the same class, however, this time for . In this case, it turns out that universality with respect to uniform convergence occurs on closed and -complement-polar sets E \subset \s. In particular, these sets of universality can have positive arc measure. In the final section, we will focus on the class . Here, we manage to prove that universality occurs on closed and -polar sets E \subset \s. Through results of Twomey [68] combined with an observation by Girela and Pélaez [23], as well as the decomposition of , we can deduce that the closed sets of universality with respect to uniform convergence of the class are characterized by -polarity. We conclude our work with an application of the latter result to the class . We will show that the closed sets of divergence for the class are given by the -polar sets
Wohnraumatlas Trier. Mietwohnungsmarkt
Full text linkDer Trierer Wohnungsmarkt ist in den vergangenen Jahren durch steigende Mieten gekennzeichnet. Dies führt zu Herausforderungen für die Bevölkerung, insbesondere für einkommensschwächere Haushalte. In diesem Atlas zeigen wir diese Entwicklung der Angebotsmieten auf und verdeutlichen, dass der Mietwohnungsmarkt in Teilmärkte segmentiert ist. Angesichts der Preissteigerungen über alle Segmente hinweg ist es notwendig, dass die Diskussion um bezahlbaren Wohnraum und gezielte stadtpolitische Maßnahmen stärker in den Fokus rückt, um langfristig eine soziale Stadtentwicklung Triers zu gewährleisten. Mit diesem Atlas wollen wir daher stadtpolitisch Aktiven und anderen Interessierten Materialien an die Hand geben, um die Wohnungspolitik der Stadt einordnen zu können
Cold pressor stress effects on cardiac repolarization
Full text linkThe cold pressor test (CPT) elicits strong cardiovascular reactions via activation of the sympathetic nervous system (SNS), yielding subsequent increases in heart rate (HR) and blood pressure (BP). However, little is known on how exposure to the CPT affects cardiac ventricular repolarization. Twenty-eight healthy males underwent both a bilateral feet CPT and a warm water (WW) control condition on two separate days, one week apart. During pre-stress baseline and stress induction cardiovascular signals (ECG lead II, Finometer BP) were monitored continuously. Salivary cortisol and subjective stress ratings were assessed intermittently. Corrected QT (QTc) interval length and T-wave amplitude (TWA) were assessed for each heartbeat and subsequently aggregated individually over baseline and stress phases, respectively. CPT increases QTc interval length and elevates the TWA. Stress-induced changes in cardiac repolarization are only in part and weakly correlated with cardiovascular and cortisol stress-reactivity. Besides its already well-established effects on cardiovascular, endocrine, and subjective responses, CPT also impacts on cardiac repolarization by elongation of QTc interval length and elevation of TWA. CPT effects on cardiac repolarization share little variance with the other indices of stress reactivity, suggesting a potentially incremental value of this parameter for understanding psychobiological adaptation to acute CPT stress