Functions Spaces And Expansions

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Functions, Spaces, and Expansions

Author : Ole Christensen
Publisher : Springer Science & Business Media
ISBN 13 : 0817649808
Total Pages : 266 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Functions, Spaces, and Expansions by : Ole Christensen

Download or read book Functions, Spaces, and Expansions written by Ole Christensen and published by Springer Science & Business Media. This book was released on 2010-05-27 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Littlewood-Paley Theory and the Study of Function Spaces

Author : Michael Frazier
Publisher : American Mathematical Soc.
ISBN 13 : 0821807315
Total Pages : 132 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Littlewood-Paley Theory and the Study of Function Spaces by : Michael Frazier

Download or read book Littlewood-Paley Theory and the Study of Function Spaces written by Michael Frazier and published by American Mathematical Soc.. This book was released on 1991 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Littlewood-Paley theory was developed to study function spaces in harmonic analysis and partial differential equations. Recently, it has contributed to the development of the $\varphi$-transform and wavelet decompositions. Based on lectures presented at the NSF-CBMS Regional Research Conference on Harmonic Analysis and Function Spaces, held at Auburn University in July 1989, this book is aimed at mathematicians, as well as mathematically literate scientists and engineers interested in harmonic analysis or wavelets. The authors provide not only a general understanding of the area of harmonic analysis relating to Littlewood-Paley theory and atomic and wavelet decompositions, but also some motivation and background helpful in understanding the recent theory of wavelets.The book begins with some simple examples which provide an overview of the classical Littlewood-Paley theory. The $\varphi$-transform, wavelet, and smooth atomic expansions are presented as natural extensions of the classical theory. Finally, applications to harmonic analysis (Calderon-Zygmund operators), signal processing (compression), and mathematical physics (potential theory) are discussed.

Expansions in Eigenfunctions of Selfadjoint Operators

Author : I͡Uriĭ Makarovich Berezanskiĭ
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886496
Total Pages : 824 pages
Book Rating : 4.8/5 (864 download)

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Book Synopsis Expansions in Eigenfunctions of Selfadjoint Operators by : I͡Uriĭ Makarovich Berezanskiĭ

Download or read book Expansions in Eigenfunctions of Selfadjoint Operators written by I͡Uriĭ Makarovich Berezanskiĭ and published by American Mathematical Soc.. This book was released on 1968 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Set Function Spaces and Orthogonal Expansions of Finitely Additive Set Functions

Author : Solomon Leader
Publisher :
ISBN 13 :
Total Pages : 130 pages
Book Rating : 4.:/5 (784 download)

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Book Synopsis Set Function Spaces and Orthogonal Expansions of Finitely Additive Set Functions by : Solomon Leader

Download or read book Set Function Spaces and Orthogonal Expansions of Finitely Additive Set Functions written by Solomon Leader and published by . This book was released on 1952 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multipliers for (C,alpha)-Bounded Fourier Expansions in Banach Spaces and Approximation Theory

Author : W. Trebels
Publisher : Springer
ISBN 13 : 3540469516
Total Pages : 110 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Multipliers for (C,alpha)-Bounded Fourier Expansions in Banach Spaces and Approximation Theory by : W. Trebels

Download or read book Multipliers for (C,alpha)-Bounded Fourier Expansions in Banach Spaces and Approximation Theory written by W. Trebels and published by Springer. This book was released on 2006-11-15 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Eigenfunction Expansions, Operator Algebras and Riemannian Symmetric Spaces

Author : Robert M Kauffman
Publisher : CRC Press
ISBN 13 : 9780582276345
Total Pages : 158 pages
Book Rating : 4.2/5 (763 download)

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Book Synopsis Eigenfunction Expansions, Operator Algebras and Riemannian Symmetric Spaces by : Robert M Kauffman

Download or read book Eigenfunction Expansions, Operator Algebras and Riemannian Symmetric Spaces written by Robert M Kauffman and published by CRC Press. This book was released on 1996-09-25 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Research Note pays particular attention to studying the convergence of the expansion and to the case where D is a family of partial differential operators. All operators in the natural von Neumann algebraassociated with D, and also unbounded operators affiliated with this algebra, are expanded simultaneously in terms of generalized eigenprojections. These are operators which carry a natural space associated with D into its dual. The elements of the range of these eigenprojections are the eigenfunctions, which solve the appropriate eigenvalue equations by duality. The spectral measure is abstractly defined, but its absolute continuity with respect to Hausdorf measure on the joint spectrum is shown to occur when the eigenfunctions are very well-behaved. Uniqueness results are given showing that any two expansions arise from each other by a simple change of variable. A considerable effort has been made to keep the book self-contained for readers with a background in functional analysis including a basic understanding of the theory of von Neumann algebras. More advanced topics in functional analysis, andan introduction to differential geometry and differential operator theory, mostly without proofs, are given in an extensive section on background material.

Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group

Author : Valery V. Volchkov
Publisher : Springer Science & Business Media
ISBN 13 : 1848825331
Total Pages : 667 pages
Book Rating : 4.8/5 (488 download)

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Book Synopsis Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group by : Valery V. Volchkov

Download or read book Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group written by Valery V. Volchkov and published by Springer Science & Business Media. This book was released on 2009-06-13 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of mean periodic functions is a subject which goes back to works of Littlewood, Delsarte, John and that has undergone a vigorous development in recent years. There has been much progress in a number of problems concerning local - pects of spectral analysis and spectral synthesis on homogeneous spaces. The study oftheseproblemsturnsouttobecloselyrelatedtoavarietyofquestionsinharmonic analysis, complex analysis, partial differential equations, integral geometry, appr- imation theory, and other branches of contemporary mathematics. The present book describes recent advances in this direction of research. Symmetric spaces and the Heisenberg group are an active ?eld of investigation at 2 the moment. The simplest examples of symmetric spaces, the classical 2-sphere S 2 and the hyperbolic plane H , play familiar roles in many areas in mathematics. The n Heisenberg groupH is a principal model for nilpotent groups, and results obtained n forH may suggest results that hold more generally for this important class of Lie groups. The purpose of this book is to develop harmonic analysis of mean periodic functions on the above spaces.

Function Spaces and Wavelets on Domains

Author : Hans Triebel
Publisher : European Mathematical Society
ISBN 13 : 9783037190197
Total Pages : 276 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Function Spaces and Wavelets on Domains by : Hans Triebel

Download or read book Function Spaces and Wavelets on Domains written by Hans Triebel and published by European Mathematical Society. This book was released on 2008 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets have emerged as an important tool in analyzing functions containing discontinuities and sharp spikes. They were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar, earthquake prediction, and pure mathematics applications such as solving partial differential equations. This book develops a theory of wavelet bases and wavelet frames for function spaces on various types of domains. Starting with the usual spaces on Euclidean spaces and their periodic counterparts, the exposition moves on to so-called thick domains (including Lipschitz domains and snowflake domains). Specifically, wavelet expansions and extensions to corresponding spaces on Euclidean $n$-spaces are developed. Finally, spaces on smooth and cellular domains and related manifolds are treated. Although the presentation relies on the recent theory of function spaces, basic notation and classical results are repeated in order to make the text self-contained. This book is addressed to two types of readers: researchers in the theory of function spaces who are interested in wavelets as new effective building blocks for functions and scientists who wish to use wavelet bases in classical function spaces for various applications. Adapted to the second type of reader, the preface contains a guide on where to find basic definitions and key assertions.

Mathematical Analysis and Applications

Author : Michael Ruzhansky
Publisher : John Wiley & Sons
ISBN 13 : 1119414334
Total Pages : 1050 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-04-11 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

The Structure of Functions

Author : Hans Triebel
Publisher : Springer Science & Business Media
ISBN 13 : 3034805691
Total Pages : 437 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Structure of Functions by : Hans Triebel

Download or read book The Structure of Functions written by Hans Triebel and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the constructive Weierstrassian approach to the theory of function spaces and various applications. The first chapter is devoted to a detailed study of quarkonial (subatomic) decompositions of functions and distributions on euclidean spaces, domains, manifolds and fractals. This approach combines the advantages of atomic and wavelet representations. It paves the way to sharp inequalities and embeddings in function spaces, spectral theory of fractal elliptic operators, and a regularity theory of some semi-linear equations. The book is self-contained, although some parts may be considered as a continuation of the author's book Fractals and Spectra. It is directed to mathematicians and (theoretical) physicists interested in the topics indicated and, in particular, how they are interrelated. - - - The book under review can be regarded as a continuation of [his book on "Fractals and spectra", 1997] (...) There are many sections named: comments, preparations, motivations, discussions and so on. These parts of the book seem to be very interesting and valuable. They help the reader to deal with the main course. (Mathematical Reviews)

Harmonic Analysis and Boundary Value Problems in the Complex Domain

Author : M.M. Djrbashian
Publisher : Birkhäuser
ISBN 13 : 3034885490
Total Pages : 258 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Harmonic Analysis and Boundary Value Problems in the Complex Domain by : M.M. Djrbashian

Download or read book Harmonic Analysis and Boundary Value Problems in the Complex Domain written by M.M. Djrbashian and published by Birkhäuser. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: As is well known, the first decades of this century were a period of elaboration of new methods in complex analysis. This elaboration had, in particular, one char acteristic feature, consisting in the interfusion of some concepts and methods of harmonic and complex analyses. That interfusion turned out to have great advan tages and gave rise to a vast number of significant results, of which we want to mention especially the classical results on the theory of Fourier series in L2 ( -7r, 7r) and their continual analog - Plancherel's theorem on the Fourier transform in L2 ( -00, +00). We want to note also two important Wiener and Paley theorems on parametric integral representations of a subclass of entire functions of expo nential type in the Hardy space H2 over a half-plane. Being under the strong influence of these results, the author began in the fifties a series of investigations in the theory of integral representations of analytic and entire functions as well as in the theory of harmonic analysis in the com plex domain. These investigations were based on the remarkable properties of the asymptotics of the entire function (p, J1 > 0), which was introduced into mathematical analysis by Mittag-Leffler for the case J1 = 1. In the process of investigation, the scope of some classical results was essentially enlarged, and the results themselves were evaluated.

From Vector Spaces to Function Spaces

Author : Yutaka Yamamoto
Publisher : SIAM
ISBN 13 : 9781611972313
Total Pages : 282 pages
Book Rating : 4.9/5 (723 download)

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Book Synopsis From Vector Spaces to Function Spaces by : Yutaka Yamamoto

Download or read book From Vector Spaces to Function Spaces written by Yutaka Yamamoto and published by SIAM. This book was released on 2012-01-01 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Theory of Besov Spaces

Author : Yoshihiro Sawano
Publisher : Springer
ISBN 13 : 9811308365
Total Pages : 945 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Theory of Besov Spaces by : Yoshihiro Sawano

Download or read book Theory of Besov Spaces written by Yoshihiro Sawano and published by Springer. This book was released on 2018-11-04 with total page 945 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multiscale Signal Analysis and Modeling

Author : Xiaoping Shen
Publisher : Springer Science & Business Media
ISBN 13 : 1461441455
Total Pages : 378 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Multiscale Signal Analysis and Modeling by : Xiaoping Shen

Download or read book Multiscale Signal Analysis and Modeling written by Xiaoping Shen and published by Springer Science & Business Media. This book was released on 2012-09-18 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiscale Signal Analysis and Modeling presents recent advances in multiscale analysis and modeling using wavelets and other systems. This book also presents applications in digital signal processing using sampling theory and techniques from various function spaces, filter design, feature extraction and classification, signal and image representation/transmission, coding, nonparametric statistical signal processing, and statistical learning theory.

Harmonic Function Theory

Author : Sheldon Axler
Publisher : Springer Science & Business Media
ISBN 13 : 1475781377
Total Pages : 266 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Harmonic Function Theory by : Sheldon Axler

Download or read book Harmonic Function Theory written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.

Operator Theory in Inner Product Spaces

Author : Karl-Heinz Förster
Publisher : Springer Science & Business Media
ISBN 13 : 3764382708
Total Pages : 240 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Operator Theory in Inner Product Spaces by : Karl-Heinz Förster

Download or read book Operator Theory in Inner Product Spaces written by Karl-Heinz Förster and published by Springer Science & Business Media. This book was released on 2007-12-03 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributions written by participants of the 4th Workshop on Operator Theory in Krein Spaces and Applications, held at the TU Berlin, Germany, December 17 to 19, 2004. The workshop covered topics from spectral, perturbation, and extension theory of linear operators and relations in inner product spaces.

Complex Analysis on Infinite Dimensional Spaces

Author : Sean Dineen
Publisher : Springer Science & Business Media
ISBN 13 : 1447108698
Total Pages : 553 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Complex Analysis on Infinite Dimensional Spaces by : Sean Dineen

Download or read book Complex Analysis on Infinite Dimensional Spaces written by Sean Dineen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional holomorphy is the study of holomorphic or analytic func tions over complex topological vector spaces. The terms in this description are easily stated and explained and allow the subject to project itself ini tially, and innocently, as a compact theory with well defined boundaries. However, a comprehensive study would include delving into, and interacting with, not only the obvious topics of topology, several complex variables theory and functional analysis but also, differential geometry, Jordan algebras, Lie groups, operator theory, logic, differential equations and fixed point theory. This diversity leads to a dynamic synthesis of ideas and to an appreciation of a remarkable feature of mathematics - its unity. Unity requires synthesis while synthesis leads to unity. It is necessary to stand back every so often, to take an overall look at one's subject and ask "How has it developed over the last ten, twenty, fifty years? Where is it going? What am I doing?" I was asking these questions during the spring of 1993 as I prepared a short course to be given at Universidade Federal do Rio de Janeiro during the following July. The abundance of suit able material made the selection of topics difficult. For some time I hesitated between two very different aspects of infinite dimensional holomorphy, the geometric-algebraic theory associated with bounded symmetric domains and Jordan triple systems and the topological theory which forms the subject of the present book.