1,720,963 research outputs found
Some remarks on non-symmetric polarization
Full text linkLet P:Cn→C be an m-homogeneous polynomial given by P(x)=∑1≤j1≤…≤jm≤ncj1…jm xj1 …xjm . Defant and Schlüters defined a non-symmetric associated m-form LP:(Cn)m→C by LP(x(1),…,x(m))=∑1≤j1≤…≤jm≤ncj1…jm xj1 (1)…xjm (m). They estimated the norm of LP on (Cn,‖⋅‖)m by the norm of P on (Cn,‖⋅‖) times a (clogn)m2 factor for every 1-unconditional norm ‖⋅‖ on Cn. A symmetrization procedure based on a card-shuffling algorithm which (together with Defant and Schlüters’ argument) brings the constant term down to (cmlogn)m−1 is provided. Regarding the lower bound, it is shown that the optimal constant is bigger than (clogn)m/2 when n≫m. Finally, the case of ℓp-norms ‖⋅‖p with 1≤p<2 is addressed.Fil: Marceca, Felipe. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin
Vector-valued general Dirichlet series
No full textOpened up by early contributions due to, among others, Besicovitch, Bohr, Bohnenblust, Hardy, Hille, Riesz, Neder and Landau, the last 20 years show a substantial revival of systematic research on ordinary Dirichlet series Pann −s , and more recently even on general Dirichlet series Pane −λns . This involves the intertwining of classical work with modern functional analysis, harmonic analysis, in nite dimensional holomorphy and probability theory as well as analytic number theory. Motivated through this line of research the main goal of this article is to start a systematic study of a variety of fundamental aspects of vector-valued general Dirichlet series Pane −λns , so Dirichlet series, where the coe cients are not necessarily in C but in some arbitrary Banach space X.Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Defant, Andreas. Universidad de Oldenburg; AlemaniaFil: Marceca, Felipe. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Schoolmann, Ingo. Universidad de Oldenburg; Alemani
Random polynomials on Banach spaces and applications to Dirichlet series
No full textEsta tesis estudia polinomios a valores vectoriales en varias variables aleatorias y aplicaciones a series de Dirichlet vectoriales. Hacer análisis en espacios de Banach requiere trasladar resultados del contexto escalar al vectorial. La validez de estos resultados generalizados depende de la estructura geométrica del espacio, que usualmente se describe en términos de objetos lineales. Los polinomios vectoriales se pueden usar para cerrar la brecha entre lo lineal y lo no lineal permitiendo así llevar a cabo este proceso de generalización que va de propiedades geométricas del espacio de Banach a resultados analíticos para funciones vectoriales. Usamos esta estrategia para obtener desigualdades del tipo Hausdorff-Young para series de Dirichlet vectoriales, relacionando la norma de una serie con la de sus coeficientes. Para lograr esto, probamos que los reconocidos conceptos de tipo y cotipo tienen una reformulación polinomial equivalente. Este resultado es de interés en sí mismo y es la contribución principal de esta tesis. Las versiones polinomiales de tipo y cotipo comparan la norma de un polinomio en varias variables aleatorias con la norma de sus coeficientes. Esta comparación se extiende a funciones vectoriales en infinitas variables y es aplicada a series de Dirichlet. Las desigualdades de decoupling desentraman estructuras de dependencia complejas de objetos aleatorios para que puedan ser analizados mediante técnicas clásicas de la teoría de variables aleatorias independientes. Para obtener versiones polinomiales de tipo y cotipo, brindamos desigualdades de decoupling para polinomios tetraedrales homogéneos. En este contexto, los polinomios se comparan con operadores multilineales asociados. Esto permite trasladar las nociones de tipo y cotipo, que son de índole lineal, al ámbito multilineal y, consecuentemente, al polinomial. Bajo condiciones geométricas más fuertes, también obtenemos desigualdades de decoupling entre polinomios aleatorios y sumas aleatorias completamente independientes de sus coeficientes. Estos resultados son llevados al contexto de series de Dirichlet y aplicados al estudio de regiones de convergencia de series de Dirichlet generales. Finalmente, el estudio del tipo y cotipo polinomiales llevó a obtener un resultado técnico de análisis asintótico. Comparamos las normas supremos de polinomios homogéneos multivariados con una versión no simétrica de la forma multilineal asociada usual.This thesis studies vector-valued polynomials in several random variables and applications to vector-valued Dirichlet series. Doing analysis on Banach spaces requires to translate results from the scalar to the vector-valued setting. The validity of these generalized results depends on the geometric structure of the Banach space which is usually described in terms of linear objects. Vector-valued polynomials can be used to close the gap between the linear and the nonlinear setting allowing to carry out this generalization procedure going from geometric properties of the Banach space to analytic results on vector-valued functions. We use this strategy to obtain Hausdorff-Young type inequalities for vector-valued Dirichlet series relating the norm of a series with the norm of its coefficients. To achieve this we show that the well-known concepts of type and cotype have an equivalent polynomial reformulation. This result is interesting on its own and is the main contribution of this thesis. The polynomial versions of type and cotype compare the norm of a polynomial in several random variables with the norm of its coefficients. This comparison is extended to vector-valued functions in infinitely many variables and applied to Dirichlet series. Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means of standard tools from the theory of independent random variables. In order to obtain the polynomial versions of type and cotype we provide decoupling inequalities for tetrahedral homogeneous polynomials. In this context, polynomials are compared with associated multilinear operators. This allows to translate the notions of type and cotype, which are linear in nature, to the multilinear and consequently the polynomial setting. Under stronger geometric assumptions we also obtain decoupling inequalities between random polynomials and fully independent random sums of its coefficients. This results are carried to the context of Dirichlet series and applied to study regions of convergence of general Dirichlet series. Finally, the study of polynomial type and cotype lead to a technical result in asymptotic analysis comparing the supremum norms of homogeneous multivariate polynomials and a non-symmetric version of the usual associated multilinear form.Fil: Marceca, Felipe. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
Random polynomials on Banach spaces and applications to Dirichlet series
Full text linkEsta tesis estudia polinomios a valores vectoriales en varias variables aleatorias y aplicaciones a series de Dirichlet vectoriales. Hacer análisis en espacios de Banach requiere trasladar resultados del contexto escalar al vectorial. La validez de estos resultados generalizados depende de la estructura geométrica del espacio, que usualmente se describe en términos de objetos lineales. Los polinomios vectoriales se pueden usar para cerrar la brecha entre lo lineal y lo no lineal permitiendo así llevar a cabo este proceso de generalización que va de propiedades geométricas del espacio de Banach a resultados analíticos para funciones vectoriales. Usamos esta estrategia para obtener desigualdades del tipo Hausdorff-Young para series de Dirichlet vectoriales, relacionando la norma de una serie con la de sus coeficientes. Para lograr esto, probamos que los reconocidos conceptos de tipo y cotipo tienen una reformulación polinomial equivalente. Este resultado es de interés en sí mismo y es la contribución principal de esta tesis. Las versiones polinomiales de tipo y cotipo comparan la norma de un polinomio en varias variables aleatorias con la norma de sus coeficientes. Esta comparación se extiende a funciones vectoriales en infinitas variables y es aplicada a series de Dirichlet. Las desigualdades de decoupling desentraman estructuras de dependencia complejas de objetos aleatorios para que puedan ser analizados mediante técnicas clásicas de la teoría de variables aleatorias independientes. Para obtener versiones polinomiales de tipo y cotipo, brindamos desigualdades de decoupling para polinomios tetraedrales homogéneos. En este contexto, los polinomios se comparan con operadores multilineales asociados. Esto permite trasladar las nociones de tipo y cotipo, que son de índole lineal, al ámbito multilineal y, consecuentemente, al polinomial. Bajo condiciones geométricas más fuertes, también obtenemos desigualdades de decoupling entre polinomios aleatorios y sumas aleatorias completamente independientes de sus coeficientes. Estos resultados son llevados al contexto de series de Dirichlet y aplicados al estudio de regiones de convergencia de series de Dirichlet generales. Finalmente, el estudio del tipo y cotipo polinomiales llevó a obtener un resultado técnico de análisis asintótico. Comparamos las normas supremos de polinomios homogéneos multivariados con una versión no simétrica de la forma multilineal asociada usual.This thesis studies vector-valued polynomials in several random variables and applications to vector-valued Dirichlet series. Doing analysis on Banach spaces requires to translate results from the scalar to the vector-valued setting. The validity of these generalized results depends on the geometric structure of the Banach space which is usually described in terms of linear objects. Vector-valued polynomials can be used to close the gap between the linear and the nonlinear setting allowing to carry out this generalization procedure going from geometric properties of the Banach space to analytic results on vector-valued functions. We use this strategy to obtain Hausdorff-Young type inequalities for vector-valued Dirichlet series relating the norm of a series with the norm of its coefficients. To achieve this we show that the well-known concepts of type and cotype have an equivalent polynomial reformulation. This result is interesting on its own and is the main contribution of this thesis. The polynomial versions of type and cotype compare the norm of a polynomial in several random variables with the norm of its coefficients. This comparison is extended to vector-valued functions in infinitely many variables and applied to Dirichlet series. Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means of standard tools from the theory of independent random variables. In order to obtain the polynomial versions of type and cotype we provide decoupling inequalities for tetrahedral homogeneous polynomials. In this context, polynomials are compared with associated multilinear operators. This allows to translate the notions of type and cotype, which are linear in nature, to the multilinear and consequently the polynomial setting. Under stronger geometric assumptions we also obtain decoupling inequalities between random polynomials and fully independent random sums of its coefficients. This results are carried to the context of Dirichlet series and applied to study regions of convergence of general Dirichlet series. Finally, the study of polynomial type and cotype lead to a technical result in asymptotic analysis comparing the supremum norms of homogeneous multivariate polynomials and a non-symmetric version of the usual associated multilinear form.Fil: Marceca, Felipe. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
- …
