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Harmonic Analysis On Homogeneous Spaces
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Book Synopsis Harmonic Analysis on Homogeneous Spaces by : Nolan R. Wallach
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.
Book Synopsis Harmonic Analysis on Spaces of Homogeneous Type by : Donggao Deng
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.
Book Synopsis Topics in Harmonic Analysis on Homogeneous Spaces by : Sigurdur Helgason
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:
Book Synopsis Harmonic Analysis on Homogeneous Spaces by : Calvin C. Moore
Download or read book Harmonic Analysis on Homogeneous Spaces written by Calvin C. Moore and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Harmonic Analysis on Homogeneous Spaces. [Edited by Calvin C. Moore]. by : Symposium in Pure Mathematics, Williams College, 1972
Download or read book Harmonic Analysis on Homogeneous Spaces. [Edited by Calvin C. Moore]. written by Symposium in Pure Mathematics, Williams College, 1972 and published by . This book was released on 1973 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric and Harmonic Analysis on Homogeneous Spaces by : Ali Baklouti
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 217 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.
Book Synopsis Representation Theory and Noncommutative Harmonic Analysis II by : A.A. Kirillov
Download or read book Representation Theory and Noncommutative Harmonic Analysis II written by A.A. Kirillov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.
Book Synopsis Harmonic Analysis of Spherical Functions on Real Reductive Groups by : Ramesh Gangolli
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.
Book Synopsis Causal Symmetric Spaces by : Gestur Olafsson
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 spaces Deals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fields Presents basic geometric properties of semi-simple symmetric spaces Includes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces
Book Synopsis Harmonic Analysis on Homogeneous Spaces by : Nolan R. Wallach
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 2018-12-12 with total page 384 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.
Book Synopsis Harmonic Maps Into Homogeneous Spaces by : Malcolm Black
Download or read book Harmonic Maps Into Homogeneous Spaces written by Malcolm Black and published by Routledge. This book was released on 2018-05-04 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps and the related theory of minimal surfaces are variational problems of long standing in differential geometry. Many important advances have been made in understanding harmonic maps of Riemann surfaces into symmetric spaces. In particular, ""twistor methods"" construct some, and in certain cases all, such mappings from holomorphic data. These notes develop techniques applicable to more general homogeneous manifolds, in particular a very general twistor result is proved. When applied to flag manifolds, this wider viewpoint allows many of the previously unrelated twistor results for symmetric spaces to be brought into a unified framework. These methods also enable a classification of harmonic maps into full flag manifolds to be established, and new examples are constructed. The techniques used are mostly a blend of the theory of compact Lie groups and complex differential geometry. This book should be of interest to mathematicians with experience in differential geometry and to theoretical physicists.
Book Synopsis Harmonic Analysis on Homogeneous Spaces by : Nolan R. Wallach
Download or read book Harmonic Analysis on Homogeneous Spaces written by Nolan R. Wallach and published by . This book was released on 1973 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric and Harmonic Analysis on Homogeneous Spaces and Applications by : Ali Baklouti
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.
Book Synopsis Harmonic Analysis on Homogeneous Spaces of SC (1,2) by : Yi. A. Verdiyev
Download or read book Harmonic Analysis on Homogeneous Spaces of SC (1,2) written by Yi. A. Verdiyev and published by . This book was released on 1988 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Harmonic Analysis on Homogeneous Spaces of SOo̳(1,2) by : Ĭ. A. Verdiev
Download or read book Harmonic Analysis on Homogeneous Spaces of SOo̳(1,2) written by Ĭ. A. Verdiev and published by . This book was released on 1988 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homogeneous Spaces and Equivariant Embeddings by : D.A. Timashev
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.
Book Synopsis A Course in Abstract Harmonic Analysis by : Gerald B. Folland
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
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