Banach Fr Chet Hilbert And Neumann Spaces
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Complex Interpolation Between Hilbert Banach And Operator Spaces
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Author : Gilles Pisier
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-10-07
Complex Interpolation Between Hilbert Banach And Operator Spaces written by Gilles Pisier and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-07 with Mathematics categories.
Motivated by a question of Vincent Lafforgue, the author studies the Banach spaces $X$ satisfying the following property: there is a function $\varepsilon\to \Delta_X(\varepsilon)$ tending to zero with $\varepsilon>0$ such that every operator $T\colon \ L_2\to L_2$ with $\T\\le \varepsilon$ that is simultaneously contractive (i.e., of norm $\le 1$) on $L_1$ and on $L_\infty$ must be of norm $\le \Delta_X(\varepsilon)$ on $L_2(X)$. The author shows that $\Delta_X(\varepsilon) \in O(\varepsilon^\alpha)$ for some $\alpha>0$ iff $X$ is isomorphic to a quotient of a subspace of an ultraproduct of $\theta$-Hilbertian spaces for some $\theta>0$ (see Corollary 6.7), where $\theta$-Hilbertian is meant in a slightly more general sense than in the author's earlier paper (1979).
A Primer On Hilbert Space Theory
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Author : Carlo Alabiso
language : en
Publisher: Springer
Release Date : 2014-10-08
A Primer On Hilbert Space Theory written by Carlo Alabiso and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-08 with Science categories.
This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all subjects has been enriched. Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
Topics In Banach Space Theory
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Author : Fernando Albiac
language : en
Publisher: Springer
Release Date : 2016-07-19
Topics In Banach Space Theory written by Fernando Albiac and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-19 with Mathematics categories.
This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book...succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly... It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments... I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book..."—Gilles Godefroy, Mathematical Reviews
Complete Second Order Linear Differential Equations In Hilbert Spaces
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Author : Alexander Ya. Shklyar
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-02-18
Complete Second Order Linear Differential Equations In Hilbert Spaces written by Alexander Ya. Shklyar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-18 with Mathematics categories.
Incomplete second order linear differential equations in Banach spaces as well as first order equations have become a classical part of functional analysis. This monograph is an attempt to present a unified systematic theory of second order equations y" (t) + Ay' (t) + By (t) = 0 including well-posedness of the Cauchy problem as well as the Dirichlet and Neumann problems. Exhaustive yet clear answers to all posed questions are given. Special emphasis is placed on new surprising effects arising for complete second order equations which do not take place for first order and incomplete second order equations. For this purpose, some new results in the spectral theory of pairs of operators and the boundary behavior of integral transforms have been developed. The book serves as a self-contained introductory course and a reference book on this subject for undergraduate and post- graduate students and research mathematicians in analysis. Moreover, users will welcome having a comprehensive study of the equations at hand, and it gives insight into the theory of complete second order linear differential equations in a general context - a theory which is far from being fully understood.
Banach Space Theory
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Author : Marián Fabian
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-04
Banach Space Theory written by Marián Fabian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-04 with Mathematics categories.
Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.
Analysis In Banach Spaces
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Author : Tuomas Hytönen
language : en
Publisher: Springer
Release Date : 2016-11-26
Analysis In Banach Spaces written by Tuomas Hytönen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-26 with Mathematics categories.
The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas.
Problems And Solutions In Banach Spaces Hilbert Spaces Fourier Transform Wavelets Generalized Functions And Quantum Mechanics
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Author : Willi-hans Steeb
language : en
Publisher: World Scientific
Release Date : 2022-08-23
Problems And Solutions In Banach Spaces Hilbert Spaces Fourier Transform Wavelets Generalized Functions And Quantum Mechanics written by Willi-hans Steeb and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-23 with Mathematics categories.
This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions.The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included.
Banach Hilbert Spaces Vector Measures And Group Representations
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Author : Tsoy-Wo Ma
language : en
Publisher: World Scientific
Release Date : 2002-01-01
Banach Hilbert Spaces Vector Measures And Group Representations written by Tsoy-Wo Ma and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
This book provides an elementary introduction to classical analysis on normed spaces, with special attention paid to fixed points, calculus, and ordinary differential equations. It contains a full treatment of vector measures on delta rings without assuming any scalar measure theory and hence should fit well into existing courses. The relation between group representations and almost periodic functions is presented. The mean values offer an infinite-dimensional analogue of measure theory on finite-dimensional Euclidean spaces. This book is ideal for beginners who want to get through the basic material as soon as possible and then do their own research immediately.
Hilbert Spaces
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Author :
language : en
Publisher: Elsevier
Release Date : 2001-07-11
Hilbert Spaces written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-11 with Mathematics categories.
This book has evolved from the lecture course on Functional Analysis I had given several times at the ETH. The text has a strict logical order, in the style of “Definition – Theorem – Proof - Example - Exercises . The proofs are rather thorough and there many examples. The first part of the book(the first three chapters, resp. the first two volumes) is devoted to the theory of Banach spaces in the most general sense of the term. The purpose of the first chapter (resp. first volume) is to introduce those results on Banach spaces which are used later or which are closely connected with the book. It therefore only contains a small part of the theory, and several results are stated (and proved) in a diluted form. The second chapter (which together with Chapter 3 makes the second volume) deals with Banach algebras (and involutive Banach algebras), which constitute the main topic of the first part of the book. The third chapter deals with compact operators on Banach spaces and linear (ordinary and partial) differential equations - applications of the, theory of Banach algebras.
Banach Spaces For Analysts
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Author : P. Wojtaszczyk
language : en
Publisher: Cambridge University Press
Release Date : 1996-08
Banach Spaces For Analysts written by P. Wojtaszczyk and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08 with Mathematics categories.
This book is intended to be used with graduate courses in Banach space theory.