A Panorama Of Harmonic Analysis
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A Panorama Of Harmonic Analysis
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Author : Steven Krantz
language : en
Publisher: Cambridge University Press
Release Date : 1999-09-02
A Panorama Of Harmonic Analysis written by Steven Krantz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-02 with Mathematics categories.
Tracing a path from the earliest beginnings of Fourier series through to the latest research A Panorama of Harmonic Analysis discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax is a consideration of ideas from the point of view of spaces of homogeneous type, which culminates in a discussion of wavelets. This book is intended for graduate students and advanced undergraduates, and mathematicians of whatever background who want a clear and concise overview of the subject of commutative harmonic analysis.
A Panorama Of Harmonic Analysis
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Author : Steven G. Krantz
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-07-03
A Panorama Of Harmonic Analysis written by Steven G. Krantz 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 2019-07-03 with Mathematics categories.
A Panorama of Harmonic Analysis treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax of the book is a consideration of the earlier ideas from the point of view of spaces of homogeneous type. The book culminates with a discussion of wavelets-one of the newest ideas in the subject. A Panorama of Harmonic Analysis is intended for graduate students, advanced undergraduates, mathematicians, and anyone wanting to get a quick overview of the subject of cummutative harmonic analysis. Applications are to mathematical physics, engineering and other parts of hard science. Required background is calculus, set theory, integration theory, and the theory of sequences and series.
A Panorama Of Harmonic Analysis
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Author :
language : en
Publisher:
Release Date : 1999
A Panorama Of Harmonic Analysis written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Harmonic Analysis
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Author : María Cristina Pereyra
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Harmonic Analysis written by María Cristina Pereyra 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 2012 with Mathematics categories.
Conveys the remarkable beauty and applicability of the ideas that have grown from Fourier theory. It presents for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization).
A First Course In Harmonic Analysis
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Author : Anton Deitmar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
A First Course In Harmonic Analysis written by Anton Deitmar 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 2013-04-17 with Mathematics categories.
This book is intended as a primer in harmonic analysis at the un dergraduate level. All the central concepts of harmonic analysis are introduced without too much technical overload. For example, the book is based entirely on the Riemann integral instead of the more demanding Lebesgue integral. Furthermore, all topological questions are dealt with purely in the context of metric spaces. It is quite sur prising that this works. Indeed, it turns out that the central concepts theory can be explained using very little of this beautiful and useful technical background. The first aim of this book is to give a lean introduction to Fourier analysis, leading up to the Poisson summation formula. The sec ond aim is to make the reader aware of the fact that both principal incarnations of Fourier Theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The third goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.
Principles Of Harmonic Analysis
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Author : Anton Deitmar
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-21
Principles Of Harmonic Analysis written by Anton Deitmar 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 2008-11-21 with Mathematics categories.
The tread of this book is formed by two fundamental principles of Harmonic Analysis: the Plancherel Formula and the Poisson S- mation Formula. We ?rst prove both for locally compact abelian groups. For non-abelian groups we discuss the Plancherel Theorem in the general situation for Type I groups. The generalization of the Poisson Summation Formula to non-abelian groups is the S- berg Trace Formula, which we prove for arbitrary groups admitting uniform lattices. As examples for the application of the Trace F- mula we treat the Heisenberg group and the group SL (R). In the 2 2 former case the trace formula yields a decomposition of the L -space of the Heisenberg group modulo a lattice. In the case SL (R), the 2 trace formula is used to derive results like the Weil asymptotic law for hyperbolic surfaces and to provide the analytic continuation of the Selberg zeta function. We ?nally include a chapter on the app- cations of abstract Harmonic Analysis on the theory of wavelets. The present book is a text book for a graduate course on abstract harmonic analysis and its applications. The book can be used as a follow up of the First Course in Harmonic Analysis, [9], or indep- dently, if the students have required a modest knowledge of Fourier Analysis already. In this book, among other things, proofs are given of Pontryagin Duality and the Plancherel Theorem for LCA-groups, which were mentioned but not proved in [9].
A Panorama Of Pure Mathematics As Seen By N Bourbaki
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Author :
language : en
Publisher: Academic Press
Release Date : 1982-08-18
A Panorama Of Pure Mathematics As Seen By N Bourbaki written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-08-18 with Mathematics categories.
A Panorama of Pure Mathematics, As Seen by N. Bourbaki
Function Theory Of One Complex Variable
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Author : Robert Everist Greene
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Function Theory Of One Complex Variable written by Robert Everist Greene 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 2006 with Mathematics categories.
Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book covers complex variables as a direct development from multivariable real calculus.
Topics In Harmonic Analysis And Ergodic Theory
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Author : Joseph Rosenblatt
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Topics In Harmonic Analysis And Ergodic Theory written by Joseph Rosenblatt 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 2007 with Mathematics categories.
There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. This text presents a series of essays on the topic.
Amenable Banach Algebras
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Author : Volker Runde
language : en
Publisher: Springer Nature
Release Date : 2020-03-03
Amenable Banach Algebras written by Volker Runde and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-03 with Mathematics categories.
This volume provides readers with a detailed introduction to the amenability of Banach algebras and locally compact groups. By encompassing important foundational material, contemporary research, and recent advancements, this monograph offers a state-of-the-art reference. It will appeal to anyone interested in questions of amenability, including those familiar with the author’s previous volume Lectures on Amenability. Cornerstone topics are covered first: namely, the theory of amenability, its historical context, and key properties of amenable groups. This introduction leads to the amenability of Banach algebras, which is the main focus of the book. Dual Banach algebras are given an in-depth exploration, as are Banach spaces, Banach homological algebra, and more. By covering amenability’s many applications, the author offers a simultaneously expansive and detailed treatment. Additionally, there are numerous exercises and notes at the end of every chapter that further elaborate on the chapter’s contents. Because it covers both the basics and cutting edge research, Amenable Banach Algebras will be indispensable to both graduate students and researchers working in functional analysis, harmonic analysis, topological groups, and Banach algebras. Instructors seeking to design an advanced course around this subject will appreciate the student-friendly elements; a prerequisite of functional analysis, abstract harmonic analysis, and Banach algebra theory is assumed.