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Author : Sigurdur Helgason
Publisher : Birkhauser
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.3/5 (91 download)
Download or read book Topics in Harmonic Analysis on Homogeneous Spaces written by Sigurdur Helgason and published by Birkhauser. This book was released on 1981 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Donggao Deng
Publisher : Springer Science & Business Media
ISBN 13 : 354088744X
Total Pages : 167 pages
Book Rating : 4.5/5 (48 download)
Download or read book Harmonic Analysis on Spaces of Homogeneous Type written by Donggao Deng and published by Springer Science & Business Media. This book was released on 2008-11-19 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book could have been entitled “Analysis and Geometry.” The authors are addressing the following issue: Is it possible to perform some harmonic analysis on a set? Harmonic analysis on groups has a long tradition. Here we are given a metric set X with a (positive) Borel measure ? and we would like to construct some algorithms which in the classical setting rely on the Fourier transformation. Needless to say, the Fourier transformation does not exist on an arbitrary metric set. This endeavor is not a revolution. It is a continuation of a line of research whichwasinitiated,acenturyago,withtwofundamentalpapersthatIwould like to discuss brie?y. The ?rst paper is the doctoral dissertation of Alfred Haar, which was submitted at to University of Gottingen ̈ in July 1907. At that time it was known that the Fourier series expansion of a continuous function may diverge at a given point. Haar wanted to know if this phenomenon happens for every 2 orthonormal basis of L [0,1]. He answered this question by constructing an orthonormal basis (today known as the Haar basis) with the property that the expansion (in this basis) of any continuous function uniformly converges to that function.
Author : Nolan R. Wallach
Publisher : Courier Dover Publications
ISBN 13 : 0486816923
Total Pages : 386 pages
Book Rating : 4.4/5 (868 download)
Download or read book Harmonic Analysis on Homogeneous Spaces written by Nolan R. Wallach and published by Courier Dover Publications. This book was released on 2018-12-18 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is suitable for advanced undergraduate and graduate students in mathematics 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, including the Peter-Weyl theorem, the theorem of the highest weight, the character theory, invariant differential operators on homogeneous vector bundles, and Bott's index theorem for such operators. Later chapters study the structure of representation theory and analysis of non-compact semi-simple Lie groups, including the principal series, intertwining operators, asymptotics of matrix coefficients, and an important special case of the Plancherel theorem. Teachers will find this volume useful as either a main text or a supplement to standard one-year courses in Lie groups and Lie algebras. The treatment advances from fairly simple topics to more complex subjects, and exercises appear at the end of each chapter. Eight helpful Appendixes develop aspects of differential geometry, Lie theory, and functional analysis employed in the main text.
Author : Ali Baklouti
Publisher : Springer Nature
ISBN 13 : 3030265625
Total Pages : 227 pages
Book Rating : 4.0/5 (32 download)
Download or read book Geometric and Harmonic Analysis on Homogeneous Spaces written by Ali Baklouti and published by Springer Nature. This book was released on 2019-08-31 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 2017 and was dedicated to the memory of the brilliant Tunisian mathematician Majdi Ben Halima. The peer-reviewed contributions selected for publication have been modified and are, without exception, of a standard equivalent to that in leading mathematical periodicals. 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.
Author : Joseph Albert Wolf
Publisher : American Mathematical Soc.
ISBN 13 : 0821842897
Total Pages : 408 pages
Book Rating : 4.8/5 (218 download)
Download or read book Harmonic Analysis on Commutative Spaces written by Joseph Albert Wolf and published by American Mathematical Soc.. This book was released on 2007 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Ramesh Gangolli
Publisher : Springer Science & Business Media
ISBN 13 : 3642729568
Total Pages : 379 pages
Book Rating : 4.6/5 (427 download)
Download or read book Harmonic Analysis of Spherical Functions on Real Reductive Groups written by Ramesh Gangolli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis on Symmetric spaces, or more generally, on homogeneous spaces of semisimple Lie groups, is a subject that has undergone a vigorous development in recent years, and has become a central part of contemporary mathematics. This is only to be expected, since homogeneous spaces and group representations arise naturally in diverse contexts ranging from Number theory and Geometry to Particle Physics and Polymer Chemistry. Its explosive growth sometimes makes it difficult to realize that it is actually relatively young as mathematical theories go. The early ideas in the subject (as is the case with many others) go back to Elie Cart an and Hermann Weyl who studied the compact symmetric spaces in the 1930's. However its full development did not begin until the 1950's when Gel'fand and Harish Chandra dared to dream of a theory of representations that included all semisimple Lie groups. Harish-Chandra's theory of spherical functions was essentially complete in the late 1950's, and was to prove to be the forerunner of his monumental work on harmonic analysis on reductive groups that has inspired a whole generation of mathematicians. It is the harmonic analysis of spherical functions on symmetric spaces, that is at the focus of this book. The fundamental questions of harmonic analysis on symmetric spaces involve an interplay of the geometric, analytical, and algebraic aspects of these spaces. They have therefore attracted a great deal of attention, and there have been many excellent expositions of the themes that are characteristic of this subject.
Author : Andreas Arvanitogeōrgos
Publisher : American Mathematical Soc.
ISBN 13 : 0821827782
Total Pages : 162 pages
Book Rating : 4.8/5 (218 download)
Download or read book An Introduction to Lie Groups and the Geometry of Homogeneous Spaces written by Andreas Arvanitogeōrgos and published by American Mathematical Soc.. This book was released on 2003 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. 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 other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and neighboring fields, such as topology, harmonic analysis, and mathematical physics.
Author : D.A. Timashev
Publisher : Springer
ISBN 13 : 9783642183980
Total Pages : 254 pages
Book Rating : 4.1/5 (839 download)
Download or read book Homogeneous Spaces and Equivariant Embeddings written by D.A. Timashev and published by Springer. This book was released on 2011-04-07 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory. By standard reasons of algebraic geometry, in order to solve various problems on a homogeneous space, it is natural and helpful to compactify it while keeping track of the group action, i.e., to consider equivariant completions or, more generally, open embeddings of a given homogeneous space. Such equivariant embeddings are the subject of this book. We focus on the classification of equivariant embeddings in terms of certain data of "combinatorial" nature (the Luna-Vust theory) and description of various geometric and representation-theoretic properties of these varieties based on these data. The class of spherical varieties, intensively studied during the last three decades, is of special interest in the scope of this book. Spherical varieties include many classical examples, such as Grassmannians, flag varieties, and varieties of quadrics, as well as well-known toric varieties. We have attempted to cover most of the important issues, including the recent substantial progress obtained in and around the theory of spherical varieties.
Author : Gerald B. Folland
Publisher : CRC Press
ISBN 13 : 1498727158
Total Pages : 317 pages
Book Rating : 4.4/5 (987 download)
Download or read book A Course in Abstract Harmonic Analysis written by Gerald B. Folland and published by CRC Press. This book was released on 2016-02-03 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul
Author : Michael Ruzhansky
Publisher : Springer
ISBN 13 : 303002895X
Total Pages : 579 pages
Book Rating : 4.0/5 (3 download)
Download or read book Hardy Inequalities on Homogeneous Groups written by Michael Ruzhansky and published by Springer. This book was released on 2019-07-02 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.
Author : Valery V. Volchkov
Publisher : Springer
ISBN 13 : 9781447122838
Total Pages : 0 pages
Book Rating : 4.1/5 (228 download)
Download or read book Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group written by Valery V. Volchkov and published by Springer. This book was released on 2011-11-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of mean periodic functions is a subject which goes back to works of Littlewood, Delsarte, John and that has undergone a vigorous development in recent years. There has been much progress in a number of problems concerning local - pects of spectral analysis and spectral synthesis on homogeneous spaces. The study oftheseproblemsturnsouttobecloselyrelatedtoavarietyofquestionsinharmonic analysis, complex analysis, partial differential equations, integral geometry, appr- imation theory, and other branches of contemporary mathematics. The present book describes recent advances in this direction of research. Symmetric spaces and the Heisenberg group are an active ?eld of investigation at 2 the moment. The simplest examples of symmetric spaces, the classical 2-sphere S 2 and the hyperbolic plane H , play familiar roles in many areas in mathematics. The n Heisenberg groupH is a principal model for nilpotent groups, and results obtained n forH may suggest results that hold more generally for this important class of Lie groups. The purpose of this book is to develop harmonic analysis of mean periodic functions on the above spaces.
Author : Gestur Olafsson
Publisher : Academic Press
ISBN 13 : 0080528724
Total Pages : 303 pages
Book Rating : 4.0/5 (85 download)
Download or read book Causal Symmetric Spaces written by Gestur Olafsson and published by Academic Press. This book was released on 1996-09-11 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to introduce researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered standard by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces.Includes the newest results in harmonic analysis including Spherical functions on ordered symmetric space and the holmorphic discrete series and Hardy spaces on compactly casual symmetric spacesDeals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fieldsPresents basic geometric properties of semi-simple symmetric spacesIncludes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces
Author : Ali Baklouti
Publisher : Springer Nature
ISBN 13 : 3030783464
Total Pages : 268 pages
Book Rating : 4.0/5 (37 download)
Download or read book Geometric and Harmonic Analysis on Homogeneous Spaces and Applications written by Ali Baklouti and published by Springer Nature. This book was released on 2021-10-29 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects a series of important works on noncommutative harmonic analysis on homogeneous spaces and related topics. All the authors participated in the 6th Tunisian-Japanese conference "Geometric and Harmonic Analysis on homogeneous spaces and Applications" held at Djerba Island in Tunisia during the period of December 16-19, 2019. The aim of this conference and the five preceding Tunisian-Japanese meetings was to keep up with the active development of representation theory interrelated with various other mathematical fields, such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations, and mathematical physics. The present volume is dedicated to the memory of Takaaki Nomura, who organized the series of Tunisian-Japanese conferences with great effort and enthusiasm. The book is a valuable resource for researchers and students working in various areas of analysis, geometry, and algebra in connection with representation theory.
Author : Dorina Mitrea
Publisher : Springer Science & Business Media
ISBN 13 : 0817683976
Total Pages : 486 pages
Book Rating : 4.8/5 (176 download)
Download or read book Groupoid Metrization Theory written by Dorina Mitrea and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry. The presentation is self-contained with complete, detailed proofs, and a large number of examples and counterexamples are provided. Unique features of Metrization Theory for Groupoids: With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis include: * treatment of metrization from a wide, interdisciplinary perspective, with accompanying applications ranging across diverse fields; * coverage of topics applicable to a variety of scientific areas within pure mathematics; * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. * coverage of topics applicable to a variety of scientific areas within pure mathematics; * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties.
Author : Yitzhak Katznelson
Publisher :
ISBN 13 :
Total Pages : 292 pages
Book Rating : 4.3/5 (91 download)
Download or read book An Introduction to Harmonic Analysis written by Yitzhak Katznelson and published by . This book was released on 1968 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Ruzhansky
Publisher : Springer Science & Business Media
ISBN 13 : 3764385146
Total Pages : 712 pages
Book Rating : 4.7/5 (643 download)
Download or read book Pseudo-Differential Operators and Symmetries written by Michael Ruzhansky and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the development of the theory of pseudo-di?erential n operators on spaces with symmetries. Such spaces are the Euclidean space R ,the n torus T , compact Lie groups and compact homogeneous spaces. The book consists of several parts. One of our aims has been not only to present new results on pseudo-di?erential operators but also to show parallels between di?erent approaches to pseudo-di?erential operators on di?erent spaces. Moreover, we tried to present the material in a self-contained way to make it accessible for readers approaching the material for the ?rst time. However, di?erent spaces on which we develop the theory of pseudo-di?er- tial operators require di?erent backgrounds. Thus, while operators on the - clidean space in Chapter 2 rely on the well-known Euclidean Fourier analysis, pseudo-di?erentialoperatorsonthetorusandmoregeneralLiegroupsinChapters 4 and 10 require certain backgrounds in discrete analysis and in the representation theory of compact Lie groups, which we therefore present in Chapter 3 and in Part III,respectively. Moreover,anyonewhowishestoworkwithpseudo-di?erential- erators on Lie groups will certainly bene?t from a good grasp of certain aspects of representation theory. That is why we present the main elements of this theory in Part III, thus eliminating the necessity for the reader to consult other sources for most of the time. Similarly, the backgrounds for the theory of pseudo-di?erential 3 operators on S and SU(2) developed in Chapter 12 can be found in Chapter 11 presented in a self-contained way suitable for immediate use.
Author : Guido Weiss
Publisher : American Mathematical Soc.
ISBN 13 : 0821814389
Total Pages : 448 pages
Book Rating : 4.8/5 (218 download)
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.
