Spherical Analysis On Harmonic An Groups

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Harmonic Analysis of Spherical Functions on Real Reductive Groups

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Author : Ramesh Gangolli
Publisher : Springer Science & Business Media
ISBN 13 : 3642729568
Total Pages : 379 pages
Book Rating : 4.6/5 (427 download)

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.

Spherical analysis on harmonic an groups

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Author : Jean-Philippe Anker
Publisher :
ISBN 13 :
Total Pages : 29 pages
Book Rating : 4.:/5 (313 download)

Book Synopsis Spherical analysis on harmonic an groups by : Jean-Philippe Anker

Download or read book Spherical analysis on harmonic an groups written by Jean-Philippe Anker and published by . This book was released on 1994 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Harmonic Analysis on Semi-Simple Lie Groups II

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Author : Garth Warner
Publisher : Springer
ISBN 13 : 9783540054696
Total Pages : 494 pages
Book Rating : 4.0/5 (546 download)

Book Synopsis Harmonic Analysis on Semi-Simple Lie Groups II by : Garth Warner

Download or read book Harmonic Analysis on Semi-Simple Lie Groups II written by Garth Warner and published by Springer. This book was released on 1972-11-23 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spherical functions and harmonic analysis on free groups

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Author : Alessandro Figà-Talamanca
Publisher :
ISBN 13 :
Total Pages : 42 pages
Book Rating : 4.:/5 (729 download)

Book Synopsis Spherical functions and harmonic analysis on free groups by : Alessandro Figà-Talamanca

Download or read book Spherical functions and harmonic analysis on free groups written by Alessandro Figà-Talamanca and published by . This book was released on 1982 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Harmonic Analysis and Special Functions on Symmetric Spaces

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Author : Gerrit Heckman
Publisher : Academic Press
ISBN 13 : 0080533299
Total Pages : 239 pages
Book Rating : 4.0/5 (85 download)

Book Synopsis Harmonic Analysis and Special Functions on Symmetric Spaces by : Gerrit Heckman

Download or read book Harmonic Analysis and Special Functions on Symmetric Spaces written by Gerrit Heckman and published by Academic Press. This book was released on 1995-02-08 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two parts of this sharply focused book, Hypergeometric and Special Functions and Harmonic Analysis on Semisimple Symmetric Spaces, are derived from lecture notes for the European School of Group Theory, a forum providing high-level courses on recent developments in group theory. The authors provide students and researchers with a thorough and thoughtful overview, elaborating on the topic with clear statements of definitions and theorems and augmenting these withtime-saving examples. An extensive set of notes supplements the text. Heckman and Schlichtkrull extend the ideas of harmonic analysis on semisimple symmetric spaces to embrace the theory of hypergeometric and spherical functions and show that the K-variant Eisenstein integrals for G/H are hypergeometric functions under this theory. They lead readers from the fundamentals of semisimple symmetric spaces of G/H to the frontier, including generalization, to the Riemannian case. This volume will interest harmonic analysts, those working on or applying the theory of symmetric spaces; it will also appeal to those with an interest in special functions. Extends ideas of harmonic analysis on symmetric spaces First treatment of the theory to include hypergeometric and spherical functions Links algebraic, analytic, and geometric methods

Groups and Geometric Analysis

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Author : Sigurdur Helgason
Publisher : American Mathematical Soc.
ISBN 13 : 0821826735
Total Pages : 693 pages
Book Rating : 4.8/5 (218 download)

Book Synopsis Groups and Geometric Analysis by : Sigurdur Helgason

Download or read book Groups and Geometric Analysis written by Sigurdur Helgason and published by American Mathematical Soc.. This book was released on 2000 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, the second of Helgason's impressive three books on Lie groups and the geometry and analysis of symmetric spaces, is an introduction to group-theoretic methods in analysis on spaces with a group action. The first chapter deals with the three two-dimensional spaces of constant curvature, requiring only elementary methods and no Lie theory. It is remarkably accessible and would be suitable for a first-year graduate course. The remainder of the book covers more advanced topics, including the work of Harish-Chandra and others, but especially that of Helgason himself. Indeed, the exposition can be seen as an account of the author's tremendous contributions to the subject.Chapter I deals with modern integral geometry and Radon transforms. The second chapter examines the interconnection between Lie groups and differential operators. Chapter IV develops the theory of spherical functions on semisimple Lie groups with a certain degree of completeness, including a study of Harish-Chandra's $c$-function. The treatment of analysis on compact symmetric spaces (Chapter V) includes some finite-dimensional representation theory for compact Lie groups and Fourier analysis on compact groups. Each chapter ends with exercises (with solutions given at the end of the book!) and historical notes.This book, which is new to the AMS publishing program, is an excellent example of the author's well-known clear and careful writing style. It has become the standard text for the study of spherical functions and invariant differential operators on symmetric spaces. Sigurdur Helgason was awarded the Steele Prize for Groups and Geometric Analysis and the companion volume, ""Differential Geometry, Lie Groups and Symmetric Spaces.""

Infinite Dimensional Spherical Analysis and Harmonic Analysis for Groups Acting on Homogeneous Trees

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Author : Emil Axelgaard
Publisher :
ISBN 13 :
Total Pages : 121 pages
Book Rating : 4.:/5 (811 download)

Book Synopsis Infinite Dimensional Spherical Analysis and Harmonic Analysis for Groups Acting on Homogeneous Trees by : Emil Axelgaard

Download or read book Infinite Dimensional Spherical Analysis and Harmonic Analysis for Groups Acting on Homogeneous Trees written by Emil Axelgaard and published by . This book was released on 2012 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Harmonic Analysis on Classical Groups

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Author : Sheng Gong
Publisher :
ISBN 13 :
Total Pages : 288 pages
Book Rating : 4.:/5 (44 download)

Book Synopsis Harmonic Analysis on Classical Groups by : Sheng Gong

Download or read book Harmonic Analysis on Classical Groups written by Sheng Gong and published by . This book was released on 1991 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Harmonic Analysis on the Heisenberg Group

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Author : Sundaram Thangavelu
Publisher : Springer Science & Business Media
ISBN 13 : 1461217725
Total Pages : 204 pages
Book Rating : 4.4/5 (612 download)

Book Synopsis Harmonic Analysis on the Heisenberg Group by : Sundaram Thangavelu

Download or read book Harmonic Analysis on the Heisenberg Group written by Sundaram Thangavelu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. 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 Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Thangavelu’s exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable.

Symmetries and Laplacians

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Author : David Gurarie
Publisher : Courier Corporation
ISBN 13 : 0486462889
Total Pages : 466 pages
Book Rating : 4.4/5 (864 download)

Book Synopsis Symmetries and Laplacians by : David Gurarie

Download or read book Symmetries and Laplacians written by David Gurarie and published by Courier Corporation. This book was released on 2007-12-21 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed as an introduction to harmonic analysis and group representations, this book examines concepts, ideas, results, and techniques related to symmetry groups and Laplacians. Its exposition is based largely on examples and applications of general theory, covering a wide range of topics rather than delving deeply into any particular area. Author David Gurarie, a Professor of Mathematics at Case Western Reserve University, focuses on discrete or continuous geometrical objects and structures, such as regular graphs, lattices, and symmetric Riemannian manifolds. Starting with the basics of representation theory, Professor Gurarie discusses commutative harmonic analysis, representations of compact and finite groups, Lie groups, and the Heisenberg group and semidirect products. Among numerous applications included are integrable hamiltonian systems, geodesic flows on symmetric spaces, and the spectral theory of the Hydrogen atom (Schrodinger operator with Coulomb potential) explicated by its Runge-Lenz symmetry. Three helpful appendixes include supplemental information, and the text concludes with references, a list of frequently used notations, and an index.

Harmonic Analysis on Free Groups

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Author : Alessandro Figa-Talamanca
Publisher : CRC Press
ISBN 13 : 1000153290
Total Pages : 164 pages
Book Rating : 4.0/5 (1 download)

Book Synopsis Harmonic Analysis on Free Groups by : Alessandro Figa-Talamanca

Download or read book Harmonic Analysis on Free Groups written by Alessandro Figa-Talamanca and published by CRC Press. This book was released on 2020-11-26 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations.

Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane

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Author : Audrey Terras
Publisher : Springer Science & Business Media
ISBN 13 : 146147972X
Total Pages : 430 pages
Book Rating : 4.4/5 (614 download)

Book Synopsis Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane by : Audrey Terras

Download or read book Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane written by Audrey Terras and published by Springer Science & Business Media. This book was released on 2013-09-12 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections and updates have been incorporated in this new edition. Updates include discussions of P. Sarnak and others' work on quantum chaos, the work of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", A. Lubotzky, R. Phillips and P. Sarnak's examples of Ramanujan graphs, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summation formula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon transform, non-Euclidean geometry on the Poincaré upper half plane H or unit disc and applications to microwave engineering, fundamental domains in H for discrete groups Γ, tessellations of H from such discrete group actions, automorphic forms, and the Selberg trace formula and its applications in spectral theory as well as number theory.

Harmonic Analysis and Integral Geometry

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Author : Massimo Picardello
Publisher : CRC Press
ISBN 13 : 0429530315
Total Pages : 194 pages
Book Rating : 4.4/5 (295 download)

Book Synopsis Harmonic Analysis and Integral Geometry by : Massimo Picardello

Download or read book Harmonic Analysis and Integral Geometry written by Massimo Picardello and published by CRC Press. This book was released on 2019-04-15 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lecture

Approximation Theory and Harmonic Analysis on Spheres and Balls

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Author : Feng Dai
Publisher : Springer Science & Business Media
ISBN 13 : 1461466601
Total Pages : 447 pages
Book Rating : 4.4/5 (614 download)

Book Synopsis Approximation Theory and Harmonic Analysis on Spheres and Balls by : Feng Dai

Download or read book Approximation Theory and Harmonic Analysis on Spheres and Balls written by Feng Dai and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.

Harmonic Analysis on Semi-Simple Lie Groups II

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Author : Garth Warner
Publisher : Springer Science & Business Media
ISBN 13 : 3642516408
Total Pages : 501 pages
Book Rating : 4.6/5 (425 download)

Book Synopsis Harmonic Analysis on Semi-Simple Lie Groups II by : Garth Warner

Download or read book Harmonic Analysis on Semi-Simple Lie Groups II written by Garth Warner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Frames and Other Bases in Abstract and Function Spaces

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Author : Isaac Pesenson
Publisher : Birkhäuser
ISBN 13 : 3319555502
Total Pages : 437 pages
Book Rating : 4.3/5 (195 download)

Book Synopsis Frames and Other Bases in Abstract and Function Spaces by : Isaac Pesenson

Download or read book Frames and Other Bases in Abstract and Function Spaces written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-06-11 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume I is organized around the theme of frames and other bases in abstract and function spaces, covering topics such as: The advanced development of frames, including Sigma-Delta quantization for fusion frames, localization of frames, and frame conditioning, as well as applications to distributed sensor networks, Galerkin-like representation of operators, scaling on graphs, and dynamical sampling. A systematic approach to shearlets with applications to wavefront sets and function spaces. Prolate and generalized prolate functions, spherical Gauss-Laguerre basis functions, and radial basis functions. Kernel methods, wavelets, and frames on compact and non-compact manifolds.

Harmonic Analysis on Homogeneous Spaces

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Author : Calvin C. Moore
Publisher : American Mathematical Society(RI)
ISBN 13 :
Total Pages : 488 pages
Book Rating : 4.F/5 ( download)

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 American Mathematical Society(RI). This book was released on 1973 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: