The Rademacher System In Function Spaces

Author : Sergey V. Astashkin
Publisher : Springer Nature
Page : 567 pages
File Size : 53,6 Mb
Release : 2020-07-27
Category : Mathematics
ISBN : 9783030478902

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The Rademacher System in Function Spaces by Sergey V. Astashkin Pdf

This book presents a systematic treatment of the Rademacher system, one of the most important unifying concepts in mathematics, and includes a number of recent important and beautiful results related to the Rademacher functions. The book discusses the relationship between the properties of the Rademacher system and geometry of some function spaces. It consists of three parts, in which this system is considered respectively in Lp-spaces, in general symmetric spaces and in certain classes of non-symmetric spaces (BMO, Paley, Cesaro, Morrey). The presentation is clear and transparent, providing all main results with detailed proofs. Moreover, literary and historical comments are given at the end of each chapter. This book will be suitable for graduate students and researchers interested in functional analysis, theory of functions and geometry of Banach spaces.

Author : Z. Semadeni
Publisher : Springer
Page : 142 pages
File Size : 55,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540391432

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Schauder Bases in Banach Spaces of Continuous Functions by Z. Semadeni Pdf

Author : Mikhail Popov,Beata Randrianantoanina
Publisher : Walter de Gruyter
Page : 336 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783110263343

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Narrow Operators on Function Spaces and Vector Lattices by Mikhail Popov,Beata Randrianantoanina Pdf

Most classes of operators that are not isomorphic embeddings are characterized by some kind of a “smallness” condition. Narrow operators are those operators defined on function spaces that are “small” at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems.

Author : Pei-Kee Lin
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 47,8 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9780817681883

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Köthe-Bochner Function Spaces by Pei-Kee Lin Pdf

This monograph is devoted to the study of Köthe–Bochner function spaces, an active area of research at the intersection of Banach space theory, harmonic analysis, probability, and operator theory. A number of significant results---many scattered throughout the literature---are distilled and presented here, giving readers a comprehensive view of the subject from its origins in functional analysis to its connections to other disciplines. Considerable background material is provided, and the theory of Köthe–Bochner spaces is rigorously developed, with a particular focus on open problems. Extensive historical information, references, and questions for further study are included; instructive examples and many exercises are incorporated throughout. Both expansive and precise, this book’s unique approach and systematic organization will appeal to advanced graduate students and researchers in functional analysis, probability, operator theory, and related fields.

Author : Александр Яковлевич Хелемский
Publisher : American Mathematical Soc.
Page : 496 pages
File Size : 44,5 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821889699

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Lectures and Exercises on Functional Analysis by Александр Яковлевич Хелемский Pdf

The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.

Author : Masami It?,Teruo Imaoka
Publisher : World Scientific
Page : 503 pages
File Size : 49,6 Mb
Release : 2003
Category : Language Arts & Disciplines
ISBN : 9789810249489

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Words, Languages, and Combinatorics Three by Masami It?,Teruo Imaoka Pdf

The research results published in this book range from pure mathematical theory (semigroup theory, discrete mathematics, etc.) to theoretical computer science, in particular formal languages and automata. The papers address issues in the algebraic and combinatorial theories of semigroups, words and languages, the structure theory of automata, the classification theory of formal languages and codes, and applications of these theories to various areas, like quantum and molecular computing, coding theory, and cryptography.

Author : Guillermo Curbera,Gerd Mockenhaupt,Werner J. Ricker
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 44,8 Mb
Release : 2010-02-21
Category : Mathematics
ISBN : 9783034602112

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Vector Measures, Integration and Related Topics by Guillermo Curbera,Gerd Mockenhaupt,Werner J. Ricker Pdf

This volume contains a selection of articles on the theme "vector measures, integration and applications" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in thearea and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, andfunctional analysis. The material is of interest to experts, young researchers and postgraduate students.

Author : Albrecht Pietsch,Jörg Wenzel
Publisher : Cambridge University Press
Page : 565 pages
File Size : 40,7 Mb
Release : 1998-09-10
Category : Mathematics
ISBN : 9780521624626

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Orthonormal Systems and Banach Space Geometry by Albrecht Pietsch,Jörg Wenzel Pdf

This book describes the interplay between orthonormal expansions and Banach space geometry.

Author : David R. Adams,Lars I. Hedberg
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783662032824

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Function Spaces and Potential Theory by David R. Adams,Lars I. Hedberg Pdf

"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society

Author : M.M. Rao,Z.D. Ren
Publisher : CRC Press
Page : 496 pages
File Size : 54,9 Mb
Release : 2002-02-08
Category : Mathematics
ISBN : 0203910869

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Applications Of Orlicz Spaces by M.M. Rao,Z.D. Ren Pdf

Presents previously unpublished material on the fundumental pronciples and properties of Orlicz sequence and function spaces. Examines the sample path behavior of stochastic processes. Provides practical applications in statistics and probability.

Author : Pei-Kee Lin
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 43,7 Mb
Release : 2003-12-12
Category : Mathematics
ISBN : 0817635211

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Köthe-Bochner Function Spaces by Pei-Kee Lin Pdf

This monograph is devoted to the study of Köthe–Bochner function spaces, an active area of research at the intersection of Banach space theory, harmonic analysis, probability, and operator theory. A number of significant results---many scattered throughout the literature---are distilled and presented here, giving readers a comprehensive view of the subject from its origins in functional analysis to its connections to other disciplines. Considerable background material is provided, and the theory of Köthe–Bochner spaces is rigorously developed, with a particular focus on open problems. Extensive historical information, references, and questions for further study are included; instructive examples and many exercises are incorporated throughout. Both expansive and precise, this book’s unique approach and systematic organization will appeal to advanced graduate students and researchers in functional analysis, probability, operator theory, and related fields.

Author : Richard M. Aron,Eva A. Gallardo Gutiérrez,Miguel Martin,Dmitry Ryabogin,Ilya M. Spitkovsky,Artem Zvavitch
Publisher : Walter de Gruyter GmbH & Co KG
Page : 397 pages
File Size : 52,7 Mb
Release : 2020-08-10
Category : Mathematics
ISBN : 9783110653465

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The Mathematical Legacy of Victor Lomonosov by Richard M. Aron,Eva A. Gallardo Gutiérrez,Miguel Martin,Dmitry Ryabogin,Ilya M. Spitkovsky,Artem Zvavitch Pdf

The fundamental contributions made by the late Victor Lomonosov in several areas of analysis are revisited in this book, in particular, by presenting new results and future directions from world-recognized specialists in the field. The invariant subspace problem, Burnside's theorem, and the Bishop-Phelps theorem are discussed in detail. This volume is an essential reference to both researchers and graduate students in mathematical analysis.

Author : Martin Buntinas
Publisher : Cambridge University Press
Page : 128 pages
File Size : 43,6 Mb
Release : 2022-01-20
Category : Mathematics
ISBN : 9781009234337

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Classical and Discrete Functional Analysis with Measure Theory by Martin Buntinas Pdf

Functional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics, chemistry, engineering, and pure mathematics. This book deals with measure theory and discrete aspects of functional analysis, including Fourier series, sequence spaces, matrix maps, and summability. Based on the author's extensive teaching experience, the text is accessible to advanced undergraduate and first-year graduate students. It can be used as a basis for a one-term course or for a one-year sequence, and is suitable for self-study for readers with an undergraduate-level understanding of real analysis and linear algebra. More than 750 exercises are included to help the reader test their understanding. Key background material is summarized in the Preliminaries.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 743 pages
File Size : 42,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789400903654

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author : Anonim
Publisher : Oxford University Press
Page : 529 pages
File Size : 44,8 Mb
Release : 2023-01-30
Category : Operator theory
ISBN : 9780192863867

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Operator Theory by Example by Anonim Pdf

Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook covers the subject through twenty examples of a wide variety of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator. The text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well-researched historical facts which place each chapter within the broader context of the development of the field as a whole.