2,123 research outputs found
Espaços Lp Não-Comutativos e Perturbações de Estados KMS
No full textWe extend the theory of perturbations of KMS states to some class of unbounded perturbations using noncommutative Lp-spaces. We also prove certain stability of the domain of the Modular Operator associated to a ||.||p-continuous state. This allows us to define an analytic multiple-time KMS condition and to obtain its analyticity together with some bounds to its norm. The main results are Theorem 5.1.15, Theorem 5.1.16 and Corollary 5.1.18. Apart from that, this work contains a detailed review, with minor contributions due to the author, starting with the description of C*-algebras and von Neumann algebras followed by weights and representations, a whole chapter is devoted to the study of KMS states and its physical interpretation as the states of thermal equilibrium, then the Tomita-Takesaki Modular Theory is presented, furthermore, we study analytical properties of the modular operator automorphism group, positive cones and bounded perturbations of states, and finally we start presenting multiple versions of noncommutative Lp-spaces.Apresentamos uma extensão da teoria de perturbações de estados KMS para uma classe de operadores ilimitados através dos espaços Lp não-comutativos. Além disso, provamos certa estabilidade do domínio do Operador Modular de um estado ||.||p-contínuo o que nos permite escrever a condições KMS para tempos múltiplos e obter sua analiticidade junto com majorantes para sua norma. Os principais resultados são o Teorema 5.1.15, o Teorema 5.1.16 e o Corolário 5.1.18. Além disso, nesse trabalho fazemos uma detalhada revisão, com contribuições menores devidas ao autor, começamos com uma descrição de álgebras C* e álgebras de von Neumann, seguida por pesos e representações, um capítulo inteiro é dedicado ao estudo de estados KMS e sua interpretação como estados de equilíbrio térmico, depois apresentamos a Teoria Modular de Tomita-Takesaki, além disso, estudamos as propriedades de analiticidade do grupo de automorfismo modular, cones positivos e perturbações de estados e finalmente, começamos a apresentar múltiplas versões dos espaços Lp não comutativos
LP-Based Identification of general nonlinear multivariable maps: Preliminary results
No full textRapport interne de GIPSA-lab. This is a preliminary work. Several versions might followIn this paper, a systematic way to approximate general nonlinear maps by means of linear programs (LP) is proposed. The argument of the map to be identified is a parameter of the LP problem while the LP-matrices are computed based on a learning data. Some examples are given to illustrate the proposed algorithm. Note that this is a working document for which several versions will be available. The author would be grateful for any constructive comments on his proposal
The Weyl calculus with respect to the Gaussian measure and restricted Lp-Lq boundedness of the Ornstein-Uhlenbeck semigroup in complex time
No full textIn this paper, we introduce a Weyl functional calculus a↦a(Q,P) for the position and momentum operators Q and P associated with the Ornstein-Uhlenbeck operator L=−Δ+x⋅∇, and give a simple criterion for restricted Lp-Lq boundedness of operators in this functional calculus. The analysis of this non-commutative functional calculus is simpler than the analysis of the functional calculus of~L. It allows us to recover, unify, and extend old and new results concerning the boundedness of exp(−zL) as an operator from Lp(Rd,γα) to Lq(Rd,γβ) for suitable values of z∈C with Rez>0, p,q∈[1,∞), and α,β>0. Here, γτ denotes the centered Gaussian measure on Rd with density (2πτ)−d/2exp(−|x|2/2τ)Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Analysi
Hyperreflexivity of the space of module homomorphisms between non-commutative Lp-spaces
No full textLet Mbe a von Neumann algebra, and let 0 <p, q≤∞. Then the space HomM(Lp(M), Lq(M))of all right M-module homomorphisms from Lp(M)to Lq(M)is a reflexive subspace of the space of all continuous linear maps from Lp(M)to Lq(M). Further, the space HomM(Lp(M), Lq(M))is hyperreflexive in each of the following cases: (i) 1 ≤q<p ≤∞; (ii) 1 ≤p, q≤∞and Mis injective, in which case the hyperreflexivity constant is at most 8.The authors were supported by project PGC2018-093794-B-I00 (MCIU/AEI/FEDER, UE), Junta de Andalucía grant FQM-185, and Proyectos I+D+i del programa operativo FEDER-Andalucía A-FQM-48-UGR18. The third named author was also supported by PhD scholarship FPU18/00419 (MIU)
Strengthening the integrality gap for the capacitated facility location problem with LP-based rounding algorithms
No full textThis thesis studies the capacitated facility location problem, in which all clients have unit demand and all facilities have integral capacity. A linear relaxation is researched, with corresponding integrality gap bounded by a constant. Recently, such a linear relaxation has been found and proven using an LP-bounding algorithm. The formulation of the relaxation and the proof were very complex and intuitively hard to understand, however. Therefore, this thesis provides a simpler, more formulation and proof. This thesis has two main contributions. First, a structured overview of all the theory prior to the construction of the relaxation is provided. To do so, the minimum knapsack problem is treated, which is a simplied version of the capacitated facility location problem. An LP-based rounding algorithm is presented to illustrate general ow-network techniques for facility location problems. Second, the rounding algorithm for the capacitated facility location problem is illustrated and explained more accessible to readers less familiar with LP-based rounding algorithms. The existing rounding algorithm for the capacitated facility location problem is treated, illustrated and extended with Matlab code. The rounding algorithm proves an integral solution for the capacitated facility location can be constructed from the linear optimal solution, with cost no more than 288 times the cost of the fractional optimal solution. This proves that the integrality gap of the proposed relaxation is bounded by 288.Electrical Engineering, Mathematics and Computer ScienceDelft Institute of Applied Mathematic
A necessary condition for the boundedness of the maximal operator on Lp(·) over reverse doubling spaces of homogeneous type
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© The Author(s) 2024.Let (X,d,μ) be a space of homogeneous type and p(·):X→[1,∞] be a variable exponent. We show that if the measure μ is Borel-semiregular and reverse doubling, then the condition essinfx∈Xp(x)>1 is necessary for the boundedness of the Hardy–Littlewood maximal operator M on the variable Lebesgue space Lp(·)(X,d,μ).publishersversionpublishe
Uniform rectifiability and ε-approximability of harmonic functions in Lp
No full textSuppose that E⊂Rn+1 is a uniformly rectifiable set of codimension 1. We show that every harmonic function is ε-approximable in Lp(Ω) for every p∈(1,∞), where Ω:=Rn+1∖E. Together with results of many authors this shows that pointwise, L∞ and Lp type ε-approximability properties of harmonic functions are all equivalent and they characterize uniform rectifiability for codimension 1 Ahlfors–David regular sets. Our results and techniques are generalizations of recent works of T. Hytönen and A. Rosén and the first author, J. M. Martell and S. Mayboroda.peerReviewe
LP-Based Identification of general nonlinear multivariable maps: Preliminary results
No full textRapport interne de GIPSA-lab. This is a preliminary work. Several versions might followIn this paper, a systematic way to approximate general nonlinear maps by means of linear programs (LP) is proposed. The argument of the map to be identified is a parameter of the LP problem while the LP-matrices are computed based on a learning data. Some examples are given to illustrate the proposed algorithm. Note that this is a working document for which several versions will be available. The author would be grateful for any constructive comments on his proposal
LP-Based Identification of general nonlinear multivariable maps: Preliminary results
No full textRapport interne de GIPSA-lab. This is a preliminary work. Several versions might followIn this paper, a systematic way to approximate general nonlinear maps by means of linear programs (LP) is proposed. The argument of the map to be identified is a parameter of the LP problem while the LP-matrices are computed based on a learning data. Some examples are given to illustrate the proposed algorithm. Note that this is a working document for which several versions will be available. The author would be grateful for any constructive comments on his proposal
The Grothendieck property of Weak Lp spaces and Marcinkiewicz spaces
No full textIn this master thesis the proof of Lotz that Weak Lp spaces have the Grothendieck property is studied. The proof is slightly modified to be more explicit and easier to comprehend by introducing lemma’s to better separate different parts of the proof that more clearly reveal its structure. Furthermore, the more general Marcinkiewicz spaces are shown to sometimes have the Grothendieck property, using the sufficient conditions for a Banach lattice to have the Grothendieck property that Lotz derived to prove the Grothendieck property of Weak Lp spaces. For most of these conditions that together are sufficient, proving that Marcinkiewicz spaces satisfy them is done in a way very similar to the case of Weak Lp spaces. However, the proof of the (necessary) condition that the dual sometimes has order continuous norm does not allow for such a simple generalization and requires more work. Finally, by using some more recent results about the existence of symmetric functionals in the dual, the conditions that are given for the Grothendieck property of Marcinkiewicz spaces are shown to be necessary, and we thereby obtain a characterization of the Marcinkiewicz spaces that have the Grothendieck propertyApplied Mathematic
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