Locally Convex Spaces And Harmonic Analysis An Introduction

Author : Philippe G. Ciarlet
Publisher : SIAM
Page : 203 pages
File Size : 45,8 Mb
Release : 2021-08-10
Category : Mathematics
ISBN : 9781611976656

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Locally Convex Spaces and Harmonic Analysis: An Introduction by Philippe G. Ciarlet Pdf

This self-contained textbook covers the fundamentals of two basic topics of linear functional analysis: locally convex spaces and harmonic analysis. Readers will find detailed introductions to topological vector spaces, distribution theory, weak topologies, the Fourier transform, the Hilbert transform, and Calderón–Zygmund singular integrals. An ideal introduction to more advanced texts, the book complements Ciarlet’s Linear and Nonlinear Functional Analysis with Applications (SIAM), in which these two topics were not treated. Pedagogical features such as detailed proofs and 93 problems make the book ideal for a one-semester first-year graduate course or for self-study. The book is intended for advanced undergraduates and first-year graduate students and researchers. It is appropriate for courses on functional analysis, distribution theory, Fourier transform, and harmonic analysis.

Author : Gerrit van Dijk
Publisher : Walter de Gruyter
Page : 234 pages
File Size : 41,6 Mb
Release : 2009-12-23
Category : Mathematics
ISBN : 9783110220209

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Introduction to Harmonic Analysis and Generalized Gelfand Pairs by Gerrit van Dijk Pdf

This book is intended as an introduction to harmonic analysis and generalized Gelfand pairs. Starting with the elementary theory of Fourier series and Fourier integrals, the author proceeds to abstract harmonic analysis on locally compact abelian groups and Gelfand pairs. Finally a more advanced theory of generalized Gelfand pairs is developed. This book is aimed at advanced undergraduates or beginning graduate students. The scope of the book is limited, with the aim of enabling students to reach a level suitable for starting PhD research. The main prerequisites for the book are elementary real, complex and functional analysis. In the later chapters, familiarity with some more advanced functional analysis is assumed, in particular with the spectral theory of (unbounded) self-adjoint operators on a Hilbert space. From the contents Fourier series Fourier integrals Locally compact groups Haar measures Harmonic analysis on locally compact abelian groups Theory and examples of Gelfand pairs Theory and examples of generalized Gelfand pairs

Author : Elias M. Stein,Guido Weiss
Publisher : Princeton University Press
Page : 312 pages
File Size : 54,9 Mb
Release : 2016-06-02
Category : Mathematics
ISBN : 9781400883899

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Introduction to Fourier Analysis on Euclidean Spaces (PMS-32), Volume 32 by Elias M. Stein,Guido Weiss Pdf

The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.

Author : S. Dineen
Publisher : Elsevier
Page : 491 pages
File Size : 44,5 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 0080871682

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Complex Analysis in Locally Convex Spaces by S. Dineen Pdf

Complex Analysis in Locally Convex Spaces

Author : Vladimir I. Bogachev,Oleg G. Smolyanov
Publisher : Springer Nature
Page : 586 pages
File Size : 53,7 Mb
Release : 2020-02-25
Category : Mathematics
ISBN : 9783030382193

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Real and Functional Analysis by Vladimir I. Bogachev,Oleg G. Smolyanov Pdf

This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.

Author : J.-P. Aubin,A. Cellina
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642695124

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Differential Inclusions by J.-P. Aubin,A. Cellina Pdf

A great impetus to study differential inclusions came from the development of Control Theory, i.e. of dynamical systems x'(t) = f(t, x(t), u(t)), x(O)=xo "controlled" by parameters u(t) (the "controls"). Indeed, if we introduce the set-valued map F(t, x)= {f(t, x, u)}ueu then solutions to the differential equations (*) are solutions to the "differen tial inclusion" (**) x'(t)EF(t, x(t)), x(O)=xo in which the controls do not appear explicitely. Systems Theory provides dynamical systems of the form d x'(t)=A(x(t)) dt (B(x(t))+ C(x(t)); x(O)=xo in which the velocity of the state of the system depends not only upon the x(t) of the system at time t, but also on variations of observations state B(x(t)) of the state. This is a particular case of an implicit differential equation f(t, x(t), x'(t)) = 0 which can be regarded as a differential inclusion (**), where the right-hand side F is defined by F(t, x)= {vlf(t, x, v)=O}. During the 60's and 70's, a special class of differential inclusions was thoroughly investigated: those of the form X'(t)E - A(x(t)), x (0) =xo where A is a "maximal monotone" map. This class of inclusions contains the class of "gradient inclusions" which generalize the usual gradient equations x'(t) = -VV(x(t)), x(O)=xo when V is a differentiable "potential". 2 Introduction There are many instances when potential functions are not differentiable

Author : Su Weiyi
Publisher : World Scientific
Page : 332 pages
File Size : 46,5 Mb
Release : 2017-08-17
Category : Mathematics
ISBN : 9789813200524

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Harmonic Analysis And Fractal Analysis Over Local Fields And Applications by Su Weiyi Pdf

This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes/textbook or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research field.The book is self-contained, with wide scope and deep knowledge, taking modern mathematics (such as modern algebra, point set topology, functional analysis, distribution theory, and so on) as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. On the other hand, the author does his best to make those difficult concepts accessible to readers, illustrate clear comparison between harmonic analysis on Euclidean spaces and that on local fields, and at the same time provide motivations underlying the new concepts and techniques. Overall, it is a high quality, up to date and valuable book for interested readers.

Author : Camil Muscalu,Wilhelm Schlag
Publisher : Cambridge University Press
Page : 341 pages
File Size : 43,9 Mb
Release : 2013-01-31
Category : Mathematics
ISBN : 9781107031821

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Classical and Multilinear Harmonic Analysis by Camil Muscalu,Wilhelm Schlag Pdf

This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.

Author : Garth Warner
Publisher : Springer Science & Business Media
Page : 545 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642502750

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Harmonic Analysis on Semi-Simple Lie Groups I by Garth Warner Pdf

The representation theory of locally compact groups has been vig orously developed in the past twenty-five years or so; of the various branches of this theory, one of the most attractive (and formidable) is the representation theory of semi-simple Lie groups which, to a great extent, is the creation of a single man: Harish-Chandra. The chief objective of the present volume and its immediate successor is to provide a reasonably self-contained introduction to Harish-Chandra's theory. Granting cer tain basic prerequisites (cf. infra), we have made an effort to give full details and complete proofs of the theorems on which the theory rests. The structure of this volume and its successor is as follows. Each book is divided into chapters; each chapter is divided into sections; each section into numbers. We then use the decimal system of reference; for example, 1. 3. 2 refers to the second number in the third section of the first chapter. Theorems, Propositions, Lemmas, and Corollaries are listed consecutively throughout any given number. Numbers which are set in fine print may be omitted at a first reading. There are a variety of Exam ples scattered throughout the text; the reader, if he is so inclined, can view them as exercises ad libitum. The Appendices to the text collect certain ancillary results which will be used on and off in the systematic exposi tion; a reference of the form A2.

Author : Garth Warner
Publisher : Springer Science & Business Media
Page : 501 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642516405

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Harmonic Analysis on Semi-Simple Lie Groups II by Garth Warner Pdf

Author : Camil Muscalu,Wilhelm Schlag
Publisher : Cambridge University Press
Page : 389 pages
File Size : 48,7 Mb
Release : 2013-01-31
Category : Mathematics
ISBN : 9781139619165

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Classical and Multilinear Harmonic Analysis: Volume 1 by Camil Muscalu,Wilhelm Schlag Pdf

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.

Author : Camil Muscalu,Wilhelm Schlag
Publisher : Cambridge University Press
Page : 341 pages
File Size : 44,8 Mb
Release : 2013-01-31
Category : Mathematics
ISBN : 9781139620468

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Classical and Multilinear Harmonic Analysis: Volume 2 by Camil Muscalu,Wilhelm Schlag Pdf

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.

Author : Semën Samsonovich Kutateladze
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 48,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401587556

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Fundamentals of Functional Analysis by Semën Samsonovich Kutateladze Pdf

to the English Translation This is a concise guide to basic sections of modern functional analysis. Included are such topics as the principles of Banach and Hilbert spaces, the theory of multinormed and uniform spaces, the Riesz-Dunford holomorphic functional calculus, the Fredholm index theory, convex analysis and duality theory for locally convex spaces. With standard provisos the presentation is self-contained, exposing about a h- dred famous "named" theorems furnished with complete proofs and culminating in the Gelfand-Nalmark-Segal construction for C*-algebras. The first Russian edition was printed by the Siberian Division of "Nauka" P- lishers in 1983. Since then the monograph has served as the standard textbook on functional analysis at the University of Novosibirsk. This volume is translated from the second Russian edition printed by the Sobolev Institute of Mathematics of the Siberian Division of the Russian Academy of Sciences· in 1995. It incorporates new sections on Radon measures, the Schwartz spaces of distributions, and a supplementary list of theoretical exercises and problems. This edition was typeset using AMS-'lEX, the American Mathematical Society's 'lEX system. To clear my conscience completely, I also confess that := stands for the definor, the assignment operator, signifies the end of the proof.

Author : Carlos A. Berenstein,Roger Gay
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461384458

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Complex Analysis and Special Topics in Harmonic Analysis by Carlos A. Berenstein,Roger Gay Pdf

A companion volume to the text "Complex Variables: An Introduction" by the same authors, this book further develops the theory, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include: Boundary values of holomorphic functions in the sense of distributions; interpolation problems and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the theorem of L. Schwarz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic function theory.

Author : Guido Weiss,Stephen Wainger
Publisher : American Mathematical Soc.
Page : 448 pages
File Size : 43,6 Mb
Release : 1979
Category : Mathematics
ISBN : 9780821814383

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Harmonic Analysis in Euclidean Spaces, Part 2 by Guido Weiss,Stephen Wainger Pdf

Contains sections on Several complex variables, Pseudo differential operators and partial differential equations, Harmonic analysis in other settings: probability, martingales, local fields, and Lie groups and functional analysis.