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Wednesday, November 25, 2020 | History

3 edition of Harmonic analysis on spaces of homogeneous type found in the catalog.

Harmonic analysis on spaces of homogeneous type

Dong-Gao Deng

Harmonic analysis on spaces of homogeneous type

  • 195 Want to read
  • 28 Currently reading

Published by Springer in Berlin .
Written in English


Edition Notes

Includes bibliographical references (p. 149-151) and index.

StatementDonggao Deng, Yongsheng Han ; with a preface by Yves Meyer
SeriesLecture notes in mathematics -- 1966
ContributionsHan, Yongsheng
Classifications
LC ClassificationsQA403 .D455 2009
The Physical Object
Paginationxii, 154 p. :
Number of Pages154
ID Numbers
Open LibraryOL24561227M
ISBN 10354088744X, 3540887458
ISBN 109783540887447, 9783540887454
LC Control Number2008938190
OCLC/WorldCa262720652

In mathematics, a weakly symmetric space is a notion introduced by the Norwegian mathematician Atle Selberg in the s as a generalisation of symmetric space, due to Élie rically the spaces are defined as complete Riemannian manifolds such that any two points can be exchanged by an isometry, the symmetric case being when the isometry is required to have period two.


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Harmonic analysis on spaces of homogeneous type by Dong-Gao Deng Download PDF EPUB FB2

"The book reflects recent trends in modern harmonic analysis on spaces of homogeneous type. is worth being read by every analyst." (Boris Rubin, Zentralblatt MATH, Vol.) “The book under review deals with real variable theory on spaces of homogeneous type.

The book does a good job of describing this theory in detail along. After many improvements, mostly achieved by the Calderón-Zygmund school, the action today is taking place in spaces of homogeneous type.

No group structure is available and the Fourier transform is missing, but a version of harmonic analysis is still available. Indeed the geometry is conducting the analysis.

"The book reflects recent trends in modern harmonic analysis on spaces of homogeneous type. is worth being read by every analyst." (Boris Rubin, Zentralblatt MATH, Vol. ) “The book under review deals with real variable theory on spaces of homogeneous type. Get this from a library. Harmonic analysis on spaces of homogeneous type.

Harmonic analysis on spaces of homogeneous type book Deng; Yongsheng Han] -- The authors succeed in generalizing the construction of wavelet bases to spaces of homogeneous type. However wavelet bases are replaced by frames, which in many applications serve the same purpose.

From the reviews:"The book reflects recent trends in modern harmonic analysis on Harmonic analysis on spaces of homogeneous type book of homogeneous type. is worth being read by every analyst." (Boris Rubin, Zentralblatt MATH, Vol. )"The book under review deals with real variable theory on spaces of homogeneous type.

1 Calderon-Zygmund Operator on Space of Homogeneous Type 9 Introduction 9 Definition of Calderon-Zygmund Operators on Spaces of Homogeneous Type 9 Littlewood-Paley Analysis on Spaces of Homogeneous Type.

15 The Tl Theorem on Spaces of Homogeneous Type 19 2 The Boundedness of Calderon-Zygmund Operators on Wavelet Spaces This book is an outgrowth of the nineteenth Summer Research Institute of the American Mathematical Society which was devoted to the topic Harmonic Analysis on Homogeneous Spaces.

Books about Harmonic Analysis on Homogeneous Spaces of SOo̳(1,2) Language: en Pages: Geometric and Harmonic Analysis on Homogeneous Spaces.

Authors: Ali Baklouti, Takaaki Nomura. Categories: Mathematics. Type: BOOK - Published: - Publisher: Springer Nature Get BOOK. Highlighting the close links between group representation theory and harmonic analysis on homogeneous spaces and numerous mathematical areas, such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations and mathematical physics, the book is intended for researchers and students working in the area of commutative and non-commutative harmonic analysis as well as group representations.

This book presents a number of important contributions focusing on harmonic analysis and representation theory of Lie groups. All were originally presented at the 5th Tunisian–Japanese conference “Geometric and Harmonic Analysis on Homogeneous Spaces and Applications”, which was held at Mahdia in Tunisia from 17 to 21 December and was dedicated to the memory of the.

This item: Harmonic Analysis on Homogeneous Spaces: Second Edition (Dover Books on Mathematics) by Nolan R. Wallach Paperback $ Only 10 left in stock (more on the way).

Ships from and sold by : Nolan R. Wallach. Harmonic Analysis on Homogeneous Spaces A.A. Kirillov, Dijk, A.U. Klimyk, A.U. Klimyk, V.F. Molchanov, V.F. Molchanov, S.Z.

Pakuliak, Vilenkin Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. The intent of this book is to give students of mathematics and mathematicians in diverse fields an entry into the subject of harmonic analysis on homogeneous spaces.

It is hoped that the book could be used as a supplement to a standard one-year course in Lie groups and Lie algebras or as the main text in a more unorthodox course on the subject. Abstract: This article is an expository paper.

We first survey developments over the past three decades in the theory of harmonic analysis on reductive symmetric spaces. Next we deal with the particular homogeneous space of non-reductive type, the so called Siegel-Jacobi space that is important arithmetically and geometrically.

This book is aimed at readers with a strong background in linear algebra and advanced calculus. Early chapters develop representation theory of compact Lie groups with applications to topology, geometry, and analysis. Later chapters study the structure of representation theory and analysis of non-compact semi-simple Lie groups.

Helpful Appendixes develop aspects of differential geometry, Lie. Orientation of this book 10 Notations in this book 13 Part 1. A bird’s-eye-view of this book 16 Function spaces appearing in harmonic analysis Part Functions on R Spaces of homogeneous type Concrete spaces Potential spaces and Sobolev spaces Lipschitz spaces Other related function spaces 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.

These are notes based very loosely on a class I gave on harmonic analysis on homogeneous spaces at the Royal Institute of Technology in Stockholm in the spring of as part of a course whose rst term was a course in integral geometry (which is why there are so many references to integral geometry). Harmonic analysis, as a subfield of analysis, is particularly interested in the Most of the material in these notes are excerpted from the book of Stein [Ste70], thebookofSteinandWeiss[SW71],thebooksofGrafakos[Gra14a,Gra14b]andthe The realization of homogeneous Besov spaces for PDEs The book presents a survey of harmonic analysis on nilpotent homogeneous spaces, results on multiplicity formulas for induced representations, new methods for constructing unitary representations of real reductive groups, and a unified treatment of trace Paley-Wiener theorems for real and \(p\)-adic reductive groups.

This book provides the latest competing research results on non-commutative harmonic analysis on homogeneous spaces with many applications. It also includes the most recent developments on other areas of mathematics including algebra and geometry.

Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the H Harmonic Analysis and Group Representations: Lectures given at a Summer Sc Harmonic Analysis on Spaces of Homogeneous Type (Lecture Notes in Mathemati New Trends in Applied Harmonic Analysis, Volume 2: Harmonic Analysis, Geome.

Wallach, Nolan R. Harmonic analysis on homogeneous spaces [by] Nolan R. Wallach M. Dekker New York Wikipedia Citation Please see Wikipedia's template documentation for further citation fields that may be required. as Damek–Ricci space. Damek–Ricci spaces are harmonic manifolds and include the class of symmetric spaces of noncompact type and real rank one properly.

Those which are not symmetric provide coun-terexamples to the Lichnerowicz conjecture [25]. Harmonic analysis on these spaces has been the object of many investigations [4, 7, 26, 27, 47].

Harmonic Analysis on Spaces of Homogeneous Type (Lecture Notes in Mathematics)的话题 (全部 条) 什么是话题 无论是一部作品、一个人,还是一件事,都往往可以衍生出许多不同的话题。. Donggao Deng and Yongsheng Han, Harmonic analysis on spaces of homogeneous type, Lecture Notes in Mathematics, vol.Springer-Verlag, Berlin, With a preface by Yves Meyer.

MR (i). A theory of holomorphic extension of eigenfunctions on homogeneous harmonic spaces is developed. Comment: 17 pages, 1 figure. (iii) S = A N with N a nilp otent group of Heisenberg-type and A. Commutative space theory is a common generalization of the theories of com­ pact topological groups, locally compact abelian groups, riemannian symmetric spaces and multiply transitive transformation groups.

This is an elegant meeting ground for group theory, harmonic analysis and differential geometry, and it even. The theory of spherical functions as eigenvalues of a Laplace (or Hecke) operator on the tree is used to introduce spherical representations and their restrictions to discrete subgroups.

This will be an excellent companion for all researchers into harmonic analysis or representation theory. 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. In this paper, the coherent states and the POV measures on tube‐type affine homogeneous phase spaces are studied.

The results extend the continuous wavelet analysis of the affine group ’ ax+b ’ and the phase space analysis of the Galilei and Poincaré groups to the general affine groups. In this paper, we first show that the remarkable orthonormal wavelet expansion for L p constructed recently by Auscher and Hytönen also converges in certain spaces of test functions and distributions.

Hence we establish the theory of product Hardy spaces on spaces X ˜ = X 1 × X 2 × ⋅ ⋅ ⋅ × X n, where each factor X i is a space of homogeneous type in the sense of Coifman and Weiss.

Harmonic analysis on spherical homogeneous spaces with solvable stabilizer Article (PDF Available) in Functional Analysis and Its Applications 46(3) September with 25 Reads.

The book was conceived as a very accessible introduction for students to materials that were only covered in textbooks at the time by the famous treatises of E.

Stein, Singular Integrals and Differentiability Properties of Functions [31], and E. Stein and G. Weiss Introduction to Fourier Analysis on Euclidean Spaces [32], which trained. Carleson Measures for Besov-Sobolev Spaces Connections to Non-Homogeneous Harmonic Analysis Main Results and Sketch of Proof T(1)-Theorem for Bergman-type operators Characterization of Carleson measures for Besov-Sobolev Spaces B.

Wick (Georgia Tech) Carleson Measures & Besov-Sobolev Spaces 3 / In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces.

In this way, he avoids the extra detail needed for a thorough discussion of representation theory. Topics in Geometric Analysis and Harmonic Analysis on Spaces of Homogeneous Type Many facets of this theory will be discussed including sharp versions of several tools used in the area of analysis on quasi-metric spaces such as a sharp Lebesgue differentiation theorem.

amounts to the ability of threading the boundary in between the two. crucible for noncommutative harmonic analysis. The point here is that the subject of harmonic analysis is a point of view and a collection of tools, and harmonic analysts continually seek new venues in which to ply their wares.

In the s E. Stein and his school intro-duced the idea of studying classical harmonic analysis—fractional. * Monge–Ampère type equations and applications * Spaces of homogeneous type * Hardy and Lipschitz spaces * One-sided operators This book will be useful to graduate students as well as pure and applied mathematicians interested in new mathematical developments in areas related to real and harmonic analysis.

This article is an expository paper. We first survey developments over the past three decades in the theory of harmonic analysis on reductive symmetric spaces. Next we deal with the particular homogeneous space of non-reductive type, the so called Siegel-Jacobi space that is important arithmetically and geometrically.

Logarithmic bump conditions for Calderón-Zygmund Operators on spaces of homogeneous type. Publicacions Mathematiques 59(1), Anderson, Theresa C.

and Vagharshakyan, Armen. A simple proof of the sharp weighted estimate for Calderon-Zygmund operators on homogeneous spaces. Journal of Geometric Analysis.The harmonic Bergman space bp() is the space of all harmonic functions uon such that kuk bp:= Z jujp d 1=p space of holomorphic functions was introduced and studied by S.

Bergman [Be]. The Bergman spaces of holomorphic functions have been and still are the object of intensive studies in harmonic analysis of functions.Motivations for the Problem Connections with Non-Homogeneous Harmonic Analysis Calder on-Zygmund Estimates for T ;2˙ These estimates on K 2˙(z;w) say that it is a Calder on-Zygmund kernel of order 2˙with respect to the metric.

Unfortunately, we can’t apply the standard T(1) technology (adapted to a space of homogeneous type) to study the.