Locally Convex Spaces And Harmonic Analysis An Introduction
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Locally Convex Spaces And Harmonic Analysis An Introduction
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Author : Philippe G. Ciarlet
language : en
Publisher: SIAM
Release Date : 2021-08-10
Locally Convex Spaces And Harmonic Analysis An Introduction written by Philippe G. Ciarlet and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-10 with Mathematics categories.
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.
Introduction To Harmonic Analysis And Generalized Gelfand Pairs
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Author : Gerrit van Dijk
language : en
Publisher: Walter de Gruyter
Release Date : 2009-12-23
Introduction To Harmonic Analysis And Generalized Gelfand Pairs written by Gerrit van Dijk 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 2009-12-23 with Mathematics categories.
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
Complex Analysis In Locally Convex Spaces
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Author : S. Dineen
language : en
Publisher: Elsevier
Release Date : 2011-08-18
Complex Analysis In Locally Convex Spaces written by S. Dineen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.
Complex Analysis in Locally Convex Spaces
Introduction To Fourier Analysis On Euclidean Spaces Pms 32 Volume 32
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Author : Elias M. Stein
language : en
Publisher: Princeton University Press
Release Date : 2016-06-02
Introduction To Fourier Analysis On Euclidean Spaces Pms 32 Volume 32 written by Elias M. Stein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-02 with Mathematics categories.
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.
The Interface Between Convex Geometry And Harmonic Analysis
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Author : Alexander Koldobsky
language : en
Publisher: American Mathematical Soc.
Release Date :
The Interface Between Convex Geometry And Harmonic Analysis written by Alexander Koldobsky 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 with Mathematics categories.
"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.
Locally Convex Spaces
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Author : Kelly McKennon
language : en
Publisher:
Release Date : 1976
Locally Convex Spaces written by Kelly McKennon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.
White Noise Calculus And Fock Space
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Author : Nobuaki Obata
language : en
Publisher: Springer
Release Date : 2006-11-15
White Noise Calculus And Fock Space written by Nobuaki Obata and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
White Noise Calculus is a distribution theory on Gaussian space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on Gaussian space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.
A Course In Functional Analysis And Measure Theory
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Author : Vladimir Kadets
language : en
Publisher: Springer
Release Date : 2018-07-10
A Course In Functional Analysis And Measure Theory written by Vladimir Kadets and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-10 with Mathematics categories.
Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory. Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses.
Harmonic Analysis In Euclidean Spaces Part 2
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Author : Guido Weiss
language : en
Publisher: American Mathematical Soc.
Release Date : 1979
Harmonic Analysis In Euclidean Spaces Part 2 written by Guido Weiss 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 1979 with Mathematics categories.
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.
Harmonic Analysis And Fractal Analysis Over Local Fields And Applications
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Author : Su Weiyi
language : en
Publisher: World Scientific
Release Date : 2017-08-17
Harmonic Analysis And Fractal Analysis Over Local Fields And Applications written by Su Weiyi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-17 with Mathematics categories.
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.