Harmonic Analysis On Symmetric Spaces And Applications I

Author : Audrey Terras
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461251286

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Harmonic Analysis on Symmetric Spaces and Applications I by Audrey Terras Pdf

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
Page : 395 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461238201

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Harmonic Analysis on Symmetric Spaces and Applications II by Audrey Terras Pdf

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 : Audrey Terras
Publisher : Unknown
Page : 128 pages
File Size : 44,8 Mb
Release : 1988
Category : Electronic
ISBN : OCLC:471847549

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Harmonic Analysis on Symmetric Spaces and Applications by Audrey Terras Pdf

Author : Audrey Terras
Publisher : Springer
Page : 500 pages
File Size : 54,5 Mb
Release : 2016-04-26
Category : Mathematics
ISBN : 9781493934089

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Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations by Audrey Terras Pdf

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 Science & Business Media
Page : 430 pages
File Size : 44,8 Mb
Release : 2013-09-12
Category : Mathematics
ISBN : 9781461479727

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

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
Page : 197 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461252986

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Hyperfunctions and Harmonic Analysis on Symmetric Spaces by Henrik Schlichtkrull Pdf

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 : Jean-Philippe Anker,Bent Orsted
Publisher : Springer Science & Business Media
Page : 183 pages
File Size : 46,9 Mb
Release : 2006-02-25
Category : Mathematics
ISBN : 9780817644260

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Lie Theory by Jean-Philippe Anker,Bent Orsted Pdf

* 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 : Audrey Terras
Publisher : Springer
Page : 368 pages
File Size : 40,8 Mb
Release : 1985-07
Category : Mathematics
ISBN : UOM:39015017335293

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Harmonic Analysis on Symmetric Spaces and Applications I by Audrey Terras Pdf

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 : Francis E. Burstall,John H. Rawnsley
Publisher : Springer
Page : 120 pages
File Size : 51,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540470526

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Twistor Theory for Riemannian Symmetric Spaces by Francis E. Burstall,John H. Rawnsley Pdf

In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces. In particular, flag manifolds are shown to arise as twistor spaces of Riemannian symmetric spaces. Applications of this theory include a complete classification of stable harmonic 2-spheres in Riemannian symmetric spaces and a Bäcklund transform for harmonic 2-spheres in Lie groups which, in many cases, provides a factorisation theorem for such spheres as well as gap phenomena. The main methods used are those of homogeneous geometry and Lie theory together with some algebraic geometry of Riemann surfaces. The work addresses differential geometers, especially those with interests in minimal surfaces and homogeneous manifolds.

Author : Jens Gerlach Christensen,Susanna Dann,Matthew Dawson
Publisher : American Mathematical Soc.
Page : 303 pages
File Size : 52,7 Mb
Release : 2018-08-27
Category : Festschriften
ISBN : 9781470440701

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Representation Theory and Harmonic Analysis on Symmetric Spaces by Jens Gerlach Christensen,Susanna Dann,Matthew Dawson Pdf

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 : Valery V. Volchkov,Vitaly V. Volchkov
Publisher : Springer Science & Business Media
Page : 667 pages
File Size : 40,7 Mb
Release : 2009-06-13
Category : Mathematics
ISBN : 9781848825338

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Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group by Valery V. Volchkov,Vitaly V. Volchkov Pdf

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,Joachim Hilgert
Publisher : Academic Press
Page : 303 pages
File Size : 48,8 Mb
Release : 1996-09-11
Category : Mathematics
ISBN : 9780080528724

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Causal Symmetric Spaces by Gestur Olafsson,Joachim Hilgert Pdf

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 : David Gurarie
Publisher : Courier Corporation
Page : 466 pages
File Size : 44,9 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780486462882

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Symmetries and Laplacians by David Gurarie Pdf

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.

Author : Joseph Albert Wolf
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 42,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821842898

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Harmonic Analysis on Commutative Spaces by Joseph Albert Wolf Pdf

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 : Ben-Zion A. Rubshtein,Genady Ya. Grabarnik,Mustafa A. Muratov,Yulia S. Pashkova
Publisher : Springer
Page : 262 pages
File Size : 51,9 Mb
Release : 2016-12-09
Category : Mathematics
ISBN : 9783319427584

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Foundations of Symmetric Spaces of Measurable Functions by Ben-Zion A. Rubshtein,Genady Ya. Grabarnik,Mustafa A. Muratov,Yulia S. Pashkova Pdf

Key definitions and results in symmetric spaces, particularly Lp, Lorentz, Marcinkiewicz and Orlicz spaces are emphasized in this textbook. A comprehensive overview of the Lorentz, Marcinkiewicz and Orlicz spaces is presented based on concepts and results of symmetric spaces. Scientists and researchers will find the application of linear operators, ergodic theory, harmonic analysis and mathematical physics noteworthy and useful. This book is intended for graduate students and researchers in mathematics and may be used as a general reference for the theory of functions, measure theory, and functional analysis. This self-contained text is presented in four parts totaling seventeen chapters to correspond with a one-semester lecture course. Each of the four parts begins with an overview and is subsequently divided into chapters, each of which concludes with exercises and notes. A chapter called “Complements” is included at the end of the text as supplementary material to assist students with independent work.