Commutative Harmonic Analysis 3
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Commutative Harmonic Analysis Iii
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Author : V.P. Havin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Commutative Harmonic Analysis Iii written by V.P. Havin 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 2012-12-06 with Mathematics categories.
The theory of generalized functions is a general method that makes it possible to consider and compute divergent integrals, sum divergent series, differentiate discontinuous functions, perform the operation of integration to any complex power and carry out other such operations that are impossible in classical analysis. Such operations are widely used in mathematical physics and the theory of differential equations, where the ideas of generalized func tions first arose, in other areas of analysis and beyond. The point of departure for this theory is to regard a function not as a mapping of point sets, but as a linear functional defined on smooth densi ties. This route leads to the loss of the concept of the value of function at a point, and also the possibility of multiplying functions, but it makes it pos sible to perform differentiation an unlimited number of times. The space of generalized functions of finite order is the minimal extension of the space of continuous functions in which coordinate differentiations are defined every where. In this sense the theory of generalized functions is a development of all of classical analysis, in particular harmonic analysis, and is to some extent the perfection of it. The more general theories of ultradistributions or gener alized functions of infinite order make it possible to consider infinite series of generalized derivatives of continuous functions.
Harmonic Analysis On Commutative Spaces
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Author : Joseph Albert Wolf
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Harmonic Analysis On Commutative Spaces written by Joseph Albert Wolf 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.
This study starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces.
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.
Commutative Harmonic Analysis I
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Author : V.P. Khavin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Commutative Harmonic Analysis I written by V.P. Khavin 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 2013-03-09 with Mathematics categories.
This volume is the first in the series devoted to the commutative harmonic analysis, a fundamental part of the contemporary mathematics. The fundamental nature of this subject, however, has been determined so long ago, that unlike in other volumes of this publication, we have to start with simple notions which have been in constant use in mathematics and physics. Planning the series as a whole, we have assumed that harmonic analysis is based on a small number of axioms, simply and clearly formulated in terms of group theory which illustrate its sources of ideas. However, our subject cannot be completely reduced to those axioms. This part of mathematics is so well developed and has so many different sides to it that no abstract scheme is able to cover its immense concreteness completely. In particular, it relates to an enormous stock of facts accumulated by the classical "trigonometric" harmonic analysis. Moreover, subjected to a general mathematical tendency of integration and diffusion of conventional intersubject borders, harmonic analysis, in its modem form, more and more rests on non-translation invariant constructions. For example, one ofthe most signifi cant achievements of latter decades, which has substantially changed the whole shape of harmonic analysis, is the penetration in this subject of subtle techniques of singular integral operators.
Principles Of Harmonic Analysis
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Author : Anton Deitmar
language : en
Publisher: Springer
Release Date : 2014-06-21
Principles Of Harmonic Analysis written by Anton Deitmar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-21 with Mathematics categories.
This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.
Harmonic Analysis On The Heisenberg Group
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Author : Sundaram Thangavelu
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-03-24
Harmonic Analysis On The Heisenberg Group written by Sundaram Thangavelu 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 1998-03-24 with Mathematics categories.
This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and, hence gives the greatest opportunity for generalizing the remarkable results of Euclidian harmonic analysis.
Analysis Iii
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Author : S. M. Nikol'skii
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Analysis Iii written by S. M. Nikol'skii 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 2013-03-09 with Mathematics categories.
In the Part at hand the authors undertake to give a presentation of the historical development of the theory of imbedding of function spaces, of the internal as well as the externals motives which have stimulated it, and of the current state of art in the field, in particular, what regards the methods employed today. The impossibility to cover all the enormous material connected with these questions inevitably forced on us the necessity to restrict ourselves to a limited circle of ideas which are both fundamental and of principal interest. Of course, such a choice had to some extent have a subjective character, being in the first place dictated by the personal interests of the authors. Thus, the Part does not constitute a survey of all contemporary questions in the theory of imbedding of function spaces. Therefore also the bibliographical references given do not pretend to be exhaustive; we only list works mentioned in the text, and a more complete bibliography can be found in appropriate other monographs. O.V. Besov, v.1. Burenkov, P.1. Lizorkin and V.G. Maz'ya have graciously read the Part in manuscript form. All their critical remarks, for which the authors hereby express their sincere thanks, were taken account of in the final editing of the manuscript.
Analysis Iv
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Author : Roger Godement
language : en
Publisher: Springer
Release Date : 2015-04-30
Analysis Iv written by Roger Godement and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-30 with Mathematics categories.
Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2). As in volumes I to III, the inimitable style of the author is recognizable here too, not only because of his refusal to write in the compact style used nowadays in many textbooks. The first part (Integration), a wise combination of mathematics said to be `modern' and `classical', is universally useful whereas the second part leads the reader towards a very active and specialized field of research, with possibly broad generalizations.
Harmonic Functions On Groups And Fourier Algebras
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Author : Cho-Ho Chu
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-05-27
Harmonic Functions On Groups And Fourier Algebras written by Cho-Ho Chu 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 2002-05-27 with Mathematics categories.
This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.
An Introduction To Harmonic Analysis
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Author : Yitzhak Katznelson
language : en
Publisher:
Release Date : 1968
An Introduction To Harmonic Analysis written by Yitzhak Katznelson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Harmonic analysis categories.