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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
11

Théorie descriptive des ensembles et espaces de Banach / Descriptive set theory and Banach spaces

Ghawadrah, Ghadeer 16 April 2015 (has links)
Cette thèse traite de la théorie descriptive des ensembles et de la géométrie des espaces de Banach. La première partie consiste en l’étude de la complexité descriptive de la famille des espaces de Banach avec la propriété d’approximation bornée, respectivement la propriété π, dans l’ensemble des sous-espaces fermés de C(Δ), où Δ est l’ensemble de Cantor. Ces familles sont boréliennes. En outre, nous montrons que si alpha<omega_{1}, l’ensemble des espaces d’indice de Szlenk au plus \alpha qui ont une FDD contractante est borélien. Nous montrons dans la seconde partie que le nombre de classes d’isomorphisme de sous-espaces complémentés des espaces d’Orlicz de fonctions réflexive L^{\Phi} [0.1] est non dénombrable, où L^{\Phi} [0.1] n’est pas isomorphe à L^2 [0,1]. / This thesis deals with the descriptive set theory and the geometry of Banach spaces.The first chapter consists of the study of the descriptive complexity of the set of Banachspaces with the Bounded Approximation Property, respectively π-property, in the set ofall closed subspaces of C(∆), where ∆ is the Cantor set. We show that these sets areBorel. In addition, we show that if α<ω_1, the set of spaces with Szlenk index at most α which have a shrinking FDD is Borel. We show in the second chapter that the numberof isomorphism classes of complemented subspaces of the reflexive Orlicz function space L^Φ [0,1] is uncountable, where L^Φ [0,1]is not isomorphic to L^2 [0,1].
12

Topologický nosič řešení stochastických diferenciálních rovnic / Topological support of solutions to stochastic differential equations

Šimon, Prokop January 2016 (has links)
No description available.
13

Interpolace logaritmicky konvexních kombinací operátorů / Interpolation of logarithmically convex combinations of operators

Takáč, Jakub January 2021 (has links)
We study the behaviour of logarithmically convex combinations of operators given by Tf = |S1f| 1 θ |S2f|1− 1 θ , where S1, S2 are some (usually quasi-linear) operators acting on spaces of measurable functions and θ ∈ (1, ∞) is a parameter. We develop two, quite different in nature, interpolation theories, each of which enables us to obtain a rather com- prehensive information about the behavior of such operators on function spaces. The first one is completely general and is based on abstract interpolation and Calderón spaces. We illustrate the theoretical results by a wide variety of examples of pairs of spaces X, Y such that T: X → Y is bounded, these in particular include the so-called Calderón-Lozanovskiı̌ construction. The second theory departs from pointwise estimates by Calderón operators and is particularly tailored for obtaining boundedness results between Orlicz spaces given weak-type estimates that arise in applications. A common feature of both theories is an approach, apparently new, involving interpolation of four spaces. The input data in each case consists of two reasonable separate endpoint estimates for the operators S1 and S2. 1
14

Weighted inequalities and properties of operators and embeddings on function spaces / Weighted inequalities and properties of operators and embeddings on function spaces

Slavíková, Lenka January 2016 (has links)
The present thesis is devoted to the study of various properties of Banach func- tion spaces, with a particular emphasis on applications in the theory of Sobolev spaces and in harmonic analysis. The thesis consists of four papers. In the first one we investigate higher-order embeddings of Sobolev-type spaces built upon rearrangement-invariant Banach function spaces. In particular, we show that optimal higher-order Sobolev embeddings follow from isoperimetric inequal- ities. In the second paper we focus on the question when the above-mentioned Sobolev-type space is a Banach algebra with respect to a pointwise multiplica- tion of functions. An embedding of the Sobolev space into the space of essentially bounded functions is proved to be the answer to this question in several standard as well as nonstandard situations. The third paper is devoted to the problem of validity of the Lebesgue differentiation theorem in the context of rearrangement- invariant Banach function spaces. We provide a necessary and sufficient condition for the validity of this theorem given in terms of concavity of certain functional depending on the norm in question and we find also alternative characterizations expressed in terms of properties of a maximal operator related to the norm. The object of the final paper is the boundedness of the...
15

Optimalita prostorů funkcí pro integrální operátor s váhou / Optimality of function spaces for a weighted integral operator

Krejčí, Jan January 2020 (has links)
This thesis studies questions related to the boundedness of the integral op- erator T : f → 1 t wf∗ , where w is a given non-increasing function and f∗ is a non-increasing rearrange- ment of a function f. The main goal is to characterize the optimal range for the operator and a given domain and conversely optimal domain for a given range. These results are then illustrated on particular examples. Lastly, some necessary conditions for the existence of optimal space are given. 1

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