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Author: Hans Triebel
Publisher: Springer Science & Business Media
ISBN: 9783764326395
Category : Science
Languages : en
Pages : 388
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Book Description
Theory of Function Spaces II deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales of spaces cover many well-known function spaces such as Hölder-Zygmund spaces, (fractional) Sobolev spaces, Besov spaces, inhomogeneous Hardy spaces, spaces of BMO-type and local approximation spaces which are closely connected with Morrey-Campanato spaces. Theory of Function Spaces II is self-contained, although it may be considered an update of the author’s earlier book of the same title. The book’s 7 chapters start with a historical survey of the subject, and then analyze the theory of function spaces in Rn and in domains, applications to (exotic) pseudo-differential operators, and function spaces on Riemannian manifolds. ------ Reviews The first chapter deserves special attention. This chapter is both an outstanding historical survey of function spaces treated in the book and a remarkable survey of rather different techniques developed in the last 50 years. It is shown that all these apparently different methods are only different ways of characterizing the same classes of functions. The book can be best recommended to researchers and advanced students working on functional analysis. - Zentralblatt MATH
Author: Hans Triebel
Publisher: Springer Science & Business Media
ISBN: 9783764326395
Category : Science
Languages : en
Pages : 388
Get Book Here
Book Description
Theory of Function Spaces II deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales of spaces cover many well-known function spaces such as Hölder-Zygmund spaces, (fractional) Sobolev spaces, Besov spaces, inhomogeneous Hardy spaces, spaces of BMO-type and local approximation spaces which are closely connected with Morrey-Campanato spaces. Theory of Function Spaces II is self-contained, although it may be considered an update of the author’s earlier book of the same title. The book’s 7 chapters start with a historical survey of the subject, and then analyze the theory of function spaces in Rn and in domains, applications to (exotic) pseudo-differential operators, and function spaces on Riemannian manifolds. ------ Reviews The first chapter deserves special attention. This chapter is both an outstanding historical survey of function spaces treated in the book and a remarkable survey of rather different techniques developed in the last 50 years. It is shown that all these apparently different methods are only different ways of characterizing the same classes of functions. The book can be best recommended to researchers and advanced students working on functional analysis. - Zentralblatt MATH
Author: Hans Triebel
Publisher: Springer Science & Business Media
ISBN: 303460419X
Category : Science
Languages : en
Pages : 376
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Book Description
Author: Hans Triebel
Publisher:
ISBN:
Category : Fourier analysis
Languages : en
Pages : 448
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Book Description
Deals with the theory of function spaces and with the developments related to the numerous applications of the theory of function spaces to some neighbouring areas such as numerics, signal processing and fractal analysis. This book discusses typical building blocks as (non-smooth) atoms, quarks, wavelet bases and wavelet frames.
Author: David R. Adams
Publisher: Springer Science & Business Media
ISBN: 3662032821
Category : Mathematics
Languages : en
Pages : 372
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Book Description
"..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: Kehe Zhu
Publisher: American Mathematical Soc.
ISBN: 0821839659
Category : Mathematics
Languages : en
Pages : 368
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Book Description
This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.
Author: Hans Triebel
Publisher: Springer Nature
ISBN: 3030358917
Category : Mathematics
Languages : en
Pages : 160
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Book Description
This book is the continuation of the "Theory of Function Spaces" trilogy, published by the same author in this series and now part of classic literature in the area of function spaces. It can be regarded as a supplement to these volumes and as an accompanying book to the textbook by D.D. Haroske and the author "Distributions, Sobolev spaces, elliptic equations".
Author: Raymond Cheng
Publisher: American Mathematical Soc.
ISBN: 1470455935
Category : Education
Languages : en
Pages : 219
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Book Description
The classical ℓp sequence spaces have been a mainstay in Banach spaces. This book reviews some of the foundational results in this area (the basic inequalities, duality, convexity, geometry) as well as connects them to the function theory (boundary growth conditions, zero sets, extremal functions, multipliers, operator theory) of the associated spaces ℓpA of analytic functions whose Taylor coefficients belong to ℓp. Relations between the Banach space ℓp and its associated function space are uncovered using tools from Banach space geometry, including Birkhoff-James orthogonality and the resulting Pythagorean inequalities. The authors survey the literature on all of this material, including a discussion of the multipliers of ℓpA and a discussion of the Wiener algebra ℓ1A. Except for some basic measure theory, functional analysis, and complex analysis, which the reader is expected to know, the material in this book is self-contained and detailed proofs of nearly all the results are given. Each chapter concludes with some end notes that give proper references, historical background, and avenues for further exploration.
Author: Yoshihiro Sawano
Publisher: Springer
ISBN: 9811308365
Category : Mathematics
Languages : en
Pages : 964
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Book Description
This is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These include a priori estimates of elliptic differential equations, the T1 theorem, pseudo-differential operators, the generator of semi-group and spaces on domains, and the Kato problem. Various function spaces are introduced to overcome the shortcomings of Besov spaces and Triebel–Lizorkin spaces as well. The only prior knowledge required of readers is familiarity with integration theory and some elementary functional analysis.Illustrations are included to show the complicated way in which spaces are defined. Owing to that complexity, many definitions are required. The necessary terminology is provided at the outset, and the theory of distributions, L^p spaces, the Hardy–Littlewood maximal operator, and the singular integral operators are called upon. One of the highlights is that the proof of the Sobolev embedding theorem is extremely simple. There are two types for each function space: a homogeneous one and an inhomogeneous one. The theory of function spaces, which readers usually learn in a standard course, can be readily applied to the inhomogeneous one. However, that theory is not sufficient for a homogeneous space; it needs to be reinforced with some knowledge of the theory of distributions. This topic, however subtle, is also covered within this volume. Additionally, related function spaces—Hardy spaces, bounded mean oscillation spaces, and Hölder continuous spaces—are defined and discussed, and it is shown that they are special cases of Besov spaces and Triebel–Lizorkin spaces.
Author: Françoise Demengel
Publisher: Springer Science & Business Media
ISBN: 1447128079
Category : Mathematics
Languages : en
Pages : 480
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Book Description
The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions. This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem. The main purpose of the book is to provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on the Schwartz space. There are complete and detailed proofs of almost all the results announced and, in some cases, more than one proof is provided in order to highlight different features of the result. Each chapter concludes with a range of exercises of varying levels of difficulty, with hints to solutions provided for many of them.
Author: Vladimir V. Tkachuk
Publisher: Springer Science & Business Media
ISBN: 1441974423
Category : Mathematics
Languages : en
Pages : 497
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Book Description
The theory of function spaces endowed with the topology of point wise convergence, or Cp-theory, exists at the intersection of three important areas of mathematics: topological algebra, functional analysis, and general topology. Cp-theory has an important role in the classification and unification of heterogeneous results from each of these areas of research. Through over 500 carefully selected problems and exercises, this volume provides a self-contained introduction to Cp-theory and general topology. By systematically introducing each of the major topics in Cp-theory, this volume is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research. Key features include: - A unique problem-based introduction to the theory of function spaces. - Detailed solutions to each of the presented problems and exercises. - A comprehensive bibliography reflecting the state-of-the-art in modern Cp-theory. - Numerous open problems and directions for further research. This volume can be used as a textbook for courses in both Cp-theory and general topology as well as a reference guide for specialists studying Cp-theory and related topics. This book also provides numerous topics for PhD specialization as well as a large variety of material suitable for graduate research.
