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Locally Convex Spaces And Harmonic Analysis An Introduction
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Book Synopsis Locally Convex Spaces and Harmonic Analysis: An Introduction by : Philippe G. Ciarlet
Download or read book Locally Convex Spaces and Harmonic Analysis: An Introduction written by Philippe G. Ciarlet and published by SIAM. This book was released on 2021-08-10 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Harmonic Analysis and Generalized Gelfand Pairs by : Gerrit van Dijk
Download or read book Introduction to Harmonic Analysis and Generalized Gelfand Pairs written by Gerrit van Dijk and published by Walter de Gruyter. This book was released on 2009-12-23 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Complex Analysis in Locally Convex Spaces by : S. Dineen
Download or read book Complex Analysis in Locally Convex Spaces written by S. Dineen and published by Elsevier. This book was released on 2011-08-18 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Analysis in Locally Convex Spaces
Book Synopsis Introduction to Fourier Analysis on Euclidean Spaces (PMS-32), Volume 32 by : Elias M. Stein
Download or read book Introduction to Fourier Analysis on Euclidean Spaces (PMS-32), Volume 32 written by Elias M. Stein and published by Princeton University Press. This book was released on 2016-06-02 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Interface Between Convex Geometry and Harmonic Analysis by : Alexander Koldobsky
Download or read book The Interface Between Convex Geometry and Harmonic Analysis written by Alexander Koldobsky and published by American Mathematical Soc.. This book was released on with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book is written in the form of lectures accessible to graduate students. This approach allows the reader to clearly see the main ideas behind the method, rather than to dwell on technical difficulties. The book also contains discussions of the most recent advances in the subject. The first section of each lecture is a snapshot of that lecture. By reading each of these sections first, novices can gain an overview of the subject, then return to the full text for more details."--BOOK JACKET.
Book Synopsis Locally Convex Spaces by : Kelly McKennon
Download or read book Locally Convex Spaces written by Kelly McKennon and published by . This book was released on 1976 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Harmonic Analysis and Convexity by : Alexander Koldobsky
Download or read book Harmonic Analysis and Convexity written by Alexander Koldobsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-07-24 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the interaction between harmonic analysis and convex geometry has increased which has resulted in solutions to several long-standing problems. This collection is based on the topics discussed during the Research Semester on Harmonic Analysis and Convexity at the Institute for Computational and Experimental Research in Mathematics in Providence RI in Fall 2022. The volume brings together experts working in related fields to report on the status of major problems in the area including the isomorphic Busemann-Petty and slicing problems for arbitrary measures, extremal problems for Fourier extension and extremal problems for classical singular integrals of martingale type, among others.
Book Synopsis Harmonic Analysis in Euclidean Spaces, Part 2 by : Guido Weiss
Download or read book Harmonic Analysis in Euclidean Spaces, Part 2 written by Guido Weiss and published by American Mathematical Soc.. This book was released on 1979 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Harmonic Analysis And Fractal Analysis Over Local Fields And Applications by : Su Weiyi
Download or read book Harmonic Analysis And Fractal Analysis Over Local Fields And Applications written by Su Weiyi and published by World Scientific. This book was released on 2017-08-17 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Real and Functional Analysis by : Vladimir I. Bogachev
Download or read book Real and Functional Analysis written by Vladimir I. Bogachev and published by Springer Nature. This book was released on 2020-02-25 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Locally Convex Spaces Over Non-Archimedean Valued Fields by : C. Perez-Garcia
Download or read book Locally Convex Spaces Over Non-Archimedean Valued Fields written by C. Perez-Garcia and published by . This book was released on 2014-05-14 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, self-contained treatment of non-Archimedean functional analysis, with an emphasis on locally convex space theory.
Book Synopsis Differential Inclusions by : J.-P. Aubin
Download or read book Differential Inclusions written by J.-P. Aubin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Classical and Multilinear Harmonic Analysis by : Camil Muscalu
Download or read book Classical and Multilinear Harmonic Analysis written by Camil Muscalu and published by Cambridge University Press. This book was released on 2013-01-31 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Book Synopsis Harmonic Analysis on Semi-Simple Lie Groups I by : Garth Warner
Download or read book Harmonic Analysis on Semi-Simple Lie Groups I written by Garth Warner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Harmonic Analysis on Semi-Simple Lie Groups II by : Garth Warner
Download or read book Harmonic Analysis on Semi-Simple Lie Groups II written by Garth Warner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classical and Multilinear Harmonic Analysis: Volume 1 by : Camil Muscalu
Download or read book Classical and Multilinear Harmonic Analysis: Volume 1 written by Camil Muscalu and published by Cambridge University Press. This book was released on 2013-01-31 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Classical and Multilinear Harmonic Analysis: Volume 2 by : Camil Muscalu
Download or read book Classical and Multilinear Harmonic Analysis: Volume 2 written by Camil Muscalu and published by Cambridge University Press. This book was released on 2013-01-31 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
