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Author : Audrey Terras
Publisher :
ISBN 13 : 9781461251293
Total Pages : 360 pages
Book Rating : 4.2/5 (512 download)
Download or read book Harmonic Analysis on Symmetric Spaces and Applications I written by Audrey Terras and published by . This book was released on 1985-06-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Audrey Terras
Publisher :
ISBN 13 : 9781461238218
Total Pages : 400 pages
Book Rating : 4.2/5 (382 download)
Download or read book Harmonic Analysis on Symmetric Spaces and Applications II written by Audrey Terras and published by . This book was released on 1988-08-01 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Audrey Terras
Publisher :
ISBN 13 : 9783540966630
Total Pages : 385 pages
Book Rating : 4.9/5 (666 download)
Download or read book Harmonic Analysis on Symmetric Spaces and Applications written by Audrey Terras and published by . This book was released on 1988-01-01 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Audrey Terras
Publisher : Springer
ISBN 13 : 1493934082
Total Pages : 500 pages
Book Rating : 4.4/5 (939 download)
Download or read book Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations written by Audrey Terras and published by Springer. This book was released on 2016-04-26 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations. It is intended for beginning graduate students in mathematics or researchers in physics or engineering. As with the introductory book entitled "Harmonic Analysis on Symmetric Spaces - Euclidean Space, the Sphere, and the Poincaré Upper Half Plane, the style is informal with an emphasis on motivation, concrete examples, history, and applications. The symmetric spaces considered here are quotients X=G/K, where G is a non-compact real Lie group, such as the general linear group GL(n,P) of all n x n non-singular real matrices, and K=O(n), the maximal compact subgroup of orthogonal matrices. Other examples are Siegel's upper half "plane" and the quaternionic upper half "plane". In the case of the general linear group, one can identify X with the space Pn of n x n positive definite symmetric matrices. Many corrections and updates have been incorporated in this new edition. Updates include discussions of random matrix theory and quantum chaos, as well as recent research on modular forms and their corresponding L-functions in higher rank. Many applications have been added, such as the solution of the heat equation on Pn, the central limit theorem of Donald St. P. Richards for Pn, results on densest lattice packing of spheres in Euclidean space, and GL(n)-analogs of the Weyl law for eigenvalues of the Laplacian in plane domains. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, fundamental domains in X for discrete groups Γ (such as the modular group GL(n,Z) of n x n matrices with integer entries and determinant ±1), connections with the problem of finding densest lattice packings of spheres in Euclidean space, automorphic forms, Hecke operators, L-functions, and the Selberg trace formula and its applications in spectral theory as well as number theory.
Author : Audrey Terras
Publisher : Springer
ISBN 13 :
Total Pages : 368 pages
Book Rating : 4.3/5 (91 download)
Download or read book Harmonic Analysis on Symmetric Spaces and Applications I written by Audrey Terras and published by Springer. This book was released on 1985-07 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its beginnings with Fourier (and as far back as the Babylonian astron omers), harmonic analysis has been developed with the goal of unraveling the mysteries of the physical world of quasars, brain tumors, and so forth, as well as the mysteries of the nonphysical, but no less concrete, world of prime numbers, diophantine equations, and zeta functions. Quoting Courant and Hilbert, in the preface to the first German edition of Methods of Mathematical Physics: "Recent trends and fashions have, however, weakened the connection between mathematics and physics." Such trends are still in evidence, harmful though they may be. My main motivation in writing these notes has been a desire to counteract this tendency towards specialization and describe appli cations of harmonic analysis in such diverse areas as number theory (which happens to be my specialty), statistics, medicine, geophysics, and quantum physics. I remember being quite surprised to learn that the subject is useful. My graduate education was that of the 1960s. The standard mathematics graduate course proceeded from Definition 1. 1. 1 to Corollary 14. 5. 59, with no room in between for applications, motivation, history, or references to related work. My aim has been to write a set of notes for a very different sort of course.
Author : Audrey Terras
Publisher : Springer Science & Business Media
ISBN 13 : 146147972X
Total Pages : 413 pages
Book Rating : 4.4/5 (614 download)
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 413 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.
Author : Henrik Schlichtkrull
Publisher : Springer Science & Business Media
ISBN 13 : 1461252989
Total Pages : 197 pages
Book Rating : 4.4/5 (612 download)
Download or read book Hyperfunctions and Harmonic Analysis on Symmetric Spaces written by Henrik Schlichtkrull and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introductory exposition of the theory of hyperfunctions and regular singularities. This first English introduction to hyperfunctions brings readers to the forefront of research in the theory of harmonic analysis on symmetric spaces. A substantial bibliography is also included. This volume is based on a paper which was awarded the 1983 University of Copenhagen Gold Medal Prize.
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 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
Author : Jean-Philippe Anker
Publisher : Springer Science & Business Media
ISBN 13 : 0817644261
Total Pages : 183 pages
Book Rating : 4.8/5 (176 download)
Download or read book Lie Theory written by Jean-Philippe Anker and published by Springer Science & Business Media. This book was released on 2006-02-25 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Presents extensive surveys by van den Ban, Schlichtkrull, and Delorme of the recent progress in deriving the Plancherel theorem on reductive symmetric spaces * Well suited for both graduate students and researchers in semisimple Lie theory and neighboring fields, possibly even mathematical cosmology * Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required
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 : Audrey Terras
Publisher : Springer Science & Business Media
ISBN 13 : 1461251281
Total Pages : 353 pages
Book Rating : 4.4/5 (612 download)
Download or read book Harmonic Analysis on Symmetric Spaces and Applications I written by Audrey Terras and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its beginnings with Fourier (and as far back as the Babylonian astron omers), harmonic analysis has been developed with the goal of unraveling the mysteries of the physical world of quasars, brain tumors, and so forth, as well as the mysteries of the nonphysical, but no less concrete, world of prime numbers, diophantine equations, and zeta functions. Quoting Courant and Hilbert, in the preface to the first German edition of Methods of Mathematical Physics: "Recent trends and fashions have, however, weakened the connection between mathematics and physics. " Such trends are still in evidence, harmful though they may be. My main motivation in writing these notes has been a desire to counteract this tendency towards specialization and describe appli cations of harmonic analysis in such diverse areas as number theory (which happens to be my specialty), statistics, medicine, geophysics, and quantum physics. I remember being quite surprised to learn that the subject is useful. My graduate eduation was that of the 1960s. The standard mathematics graduate course proceeded from Definition 1. 1. 1 to Corollary 14. 5. 59, with no room in between for applications, motivation, history, or references to related work. My aim has been to write a set of notes for a very different sort of course.
Author : Audrey Terras
Publisher : Springer Science & Business Media
ISBN 13 : 146123820X
Total Pages : 395 pages
Book Rating : 4.4/5 (612 download)
Download or read book Harmonic Analysis on Symmetric Spaces and Applications II written by Audrey Terras and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Well, finally, here it is-the long-promised "Revenge of the Higher Rank Symmetric Spaces and Their Fundamental Domains." When I began work on it in 1977, I would probably have stopped immediately if someone had told me that ten years would pass before I would declare it "finished." Yes, I am declaring it finished-though certainly not perfected. There is a large amount of work going on at the moment as the piles of preprints reach the ceiling. Nevertheless, it is summer and the ocean calls. So I am not going to spend another ten years revising and polishing. But, gentle reader, do send me your corrections and even your preprints. Thanks to your work, there is an Appendix at the end of this volume with corrections to Volume I. I said it all in the Preface to Volume I. So I will try not to repeat myself here. Yes, the "recent trends" mentioned in that Preface are still just as recent.
Author : Nolan R. Wallach
Publisher : Courier Dover Publications
ISBN 13 : 0486836436
Total Pages : 384 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 2018-12-12 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.
Author : Yves Guivarc'h
Publisher : Springer Science & Business Media
ISBN 13 : 1461224527
Total Pages : 297 pages
Book Rating : 4.4/5 (612 download)
Download or read book Compactifications of Symmetric Spaces written by Yves Guivarc'h and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of symmetric space is of central importance in many branches of mathematics. Compactifications of these spaces have been studied from the points of view of representation theory, geometry, and random walks. This work is devoted to the study of the interrelationships among these various compactifications and, in particular, focuses on the martin compactifications. It is the first exposition to treat compactifications of symmetric spaces systematically and to uniformized the various points of view. The work is largely self-contained, with comprehensive references to the literature. It is an excellent resource for both researchers and graduate students.
Author : Valery V. Volchkov
Publisher : Springer Science & Business Media
ISBN 13 : 1848825331
Total Pages : 667 pages
Book Rating : 4.8/5 (488 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 Science & Business Media. This book was released on 2009-06-13 with total page 667 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 : Jens Gerlach Christensen
Publisher : American Mathematical Soc.
ISBN 13 : 1470440709
Total Pages : 303 pages
Book Rating : 4.4/5 (74 download)
Download or read book Representation Theory and Harmonic Analysis on Symmetric Spaces written by Jens Gerlach Christensen and published by American Mathematical Soc.. This book was released on 2018-08-27 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Harmonic Analysis, in honor of Gestur Ólafsson's 65th birthday, held on January 4, 2017, in Atlanta, Georgia. The articles in this volume provide fresh perspectives on many different directions within harmonic analysis, highlighting the connections between harmonic analysis and the areas of integral geometry, complex analysis, operator algebras, Lie algebras, special functions, and differential operators. The breadth of contributions highlights the diversity of current research in harmonic analysis and shows that it continues to be a vibrant and fruitful field of inquiry.
Author : Sigurdur Helgason
Publisher : American Mathematical Soc.
ISBN 13 : 9780821874875
Total Pages : 670 pages
Book Rating : 4.8/5 (748 download)
Download or read book Geometric Analysis on Symmetric Spaces written by Sigurdur Helgason and published by American Mathematical Soc.. This book was released on 1993 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt:
