Function Spaces In Analysis

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From Vector Spaces To Function Spaces

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Author : Yutaka Yamamoto
language : en
Publisher: SIAM
Release Date : 2012-01-01

From Vector Spaces To Function Spaces written by Yutaka Yamamoto and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-01 with Mathematics categories.

This book provides a treatment of analytical methods of applied mathematics. It starts with a review of the basics of vector spaces and brings the reader to an advanced discussion of applied mathematics, including the latest applications to systems and control theory. The text is designed to be accessible to those not familiar with the material and useful to working scientists, engineers, and mathematics students. The author provides the motivations of definitions and the ideas underlying proofs but does not sacrifice mathematical rigor. From Vector Spaces to Function Spaces presents: an easily accessible discussion of analytical methods of applied mathematics from vector spaces to distributions, Fourier analysis, and Hardy spaces with applications to system theory; an introduction to modern functional analytic methods to better familiarize readers with basic methods and mathematical thinking; and an understandable yet penetrating treatment of such modern methods and topics as function spaces and distributions, Fourier and Laplace analyses, and Hardy spaces.

Function Spaces And Potential Theory

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Author : David R. Adams
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-11-22

Function Spaces And Potential Theory written by David R. Adams 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 1999-11-22 with Mathematics categories.

"..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

Functions Spaces And Expansions

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Author : Ole Christensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-27

Functions Spaces And Expansions written by Ole Christensen 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 2010-05-27 with Mathematics categories.

This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required.

Analysis On Fock Spaces

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Author : Kehe Zhu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-05-26

Analysis On Fock Spaces written by Kehe Zhu 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 2012-05-26 with Mathematics categories.

Several natural Lp spaces of analytic functions have been widely studied in the past few decades, including Hardy spaces, Bergman spaces, and Fock spaces. The terms “Hardy spaces” and “Bergman spaces” are by now standard and well established. But the term “Fock spaces” is a different story. Numerous excellent books now exist on the subject of Hardy spaces. Several books about Bergman spaces, including some of the author’s, have also appeared in the past few decades. But there has been no book on the market concerning the Fock spaces. The purpose of this book is to fill that void, especially when many results in the subject are complete by now. This book presents important results and techniques summarized in one place, so that new comers, especially graduate students, have a convenient reference to the subject. This book contains proofs that are new and simpler than the existing ones in the literature. In particular, the book avoids the use of the Heisenberg group, the Fourier transform, and the heat equation. This helps to keep the prerequisites to a minimum. A standard graduate course in each of real analysis, complex analysis, and functional analysis should be sufficient preparation for the reader.

Functional Analysis In Asymmetric Normed Spaces

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Author : Stefan Cobzas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-30

Functional Analysis In Asymmetric Normed Spaces written by Stefan Cobzas 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 2012-10-30 with Mathematics categories.

An asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm p is translation invariant so that the addition is continuous, but the asymmetry of the norm implies that the multiplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of X, meaning the set of all real-valued upper semi-continuous linear functionals on X, is merely a convex cone in the vector space of all linear functionals on X. In spite of these differences, many results from classical functional analysis have their counterparts in the asymmetric case, by taking care of the interplay between the asymmetric norm p and its conjugate. Among the positive results one can mention: Hahn–Banach type theorems and separation results for convex sets, Krein–Milman type theorems, analogs of the fundamental principles – open mapping, closed graph and uniform boundedness theorems – an analog of the Schauder’s theorem on the compactness of the conjugate mapping. Applications are given to best approximation problems and, as relevant examples, one considers normed lattices equipped with asymmetric norms and spaces of semi-Lipschitz functions on quasi-metric spaces. Since the basic topological tools come from quasi-metric spaces and quasi-uniform spaces, the first chapter of the book contains a detailed presentation of some basic results from the theory of these spaces. The focus is on results which are most used in functional analysis – completeness, compactness and Baire category – which drastically differ from those in metric or uniform spaces. The book is fairly self-contained, the prerequisites being the acquaintance with the basic results in topology and functional analysis, so it may be used for an introduction to the subject. Since new results, in the focus of current research, are also included, researchers in the area can use it as a reference text.

Function Spaces 1

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Author : Luboš Pick
language : en
Publisher: Walter de Gruyter
Release Date : 2012-12-19

Function Spaces 1 written by Luboš Pick and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-19 with Mathematics categories.

This is the first part of the second revised and extended edition of the well established book "Function Spaces" by Alois Kufner, Oldřich John, and Svatopluk Fučík. Like the first edition this monograph is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces in their research or lecture courses. This first volume is devoted to the study of function spaces, based on intrinsic properties of a function such as its size, continuity, smoothness, various forms of a control over the mean oscillation, and so on. The second volume will be dedicated to the study of function spaces of Sobolev type, in which the key notion is the weak derivative of a function of several variables.

Linear Processes In Function Spaces

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Author : Denis Bosq
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Linear Processes In Function Spaces written by Denis Bosq 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 2012-12-06 with Mathematics categories.

The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. The necessary mathematical tools are presented in Chapters 1 and 2. Chapters 3 to 6 deal with autoregressive processes in Hilbert and Banach spaces. Chapter 7 is devoted to general linear processes and Chapter 8 with statistical prediction. Implementation and numerical applications appear in Chapter 9. The book assumes a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the University of Paris 6 (Pierre et Marie Curie). He is Chief-Editor of Statistical Inference for Stochastic Processes and of Annales de l'ISUP, and Associate Editor of the Journal of Nonparametric Statistics. He is an elected member of the International Statistical Institute, and he has published about 100 papers or works on nonparametric statistics and five books including Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, Second Edition (Springer, 1998).

Theory Of Function Spaces Ii

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Author : Hans Triebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-16

Theory Of Function Spaces Ii written by Hans Triebel 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 2010-08-16 with Juvenile Nonfiction categories.

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

Function Spaces In Modern Analysis

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Author : Krzysztof Jarosz
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-07-18

Function Spaces In Modern Analysis written by Krzysztof Jarosz 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 2011-07-18 with Mathematics categories.

This volume contains the proceedings of the Sixth Conference on Function Spaces, which was held from May 18-22, 2010, at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.

Functional Analysis And Applied Optimization In Banach Spaces

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Author : Fabio Botelho
language : en
Publisher: Springer
Release Date : 2014-06-12

Functional Analysis And Applied Optimization In Banach Spaces written by Fabio Botelho and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-12 with Mathematics categories.

​This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.