Harmonic Analysis Of Spherical Functions On Real Reductive Groups

Author : Ramesh Gangolli,Veeravalli S. Varadarajan
Publisher : Springer Science & Business Media
Page : 379 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642729560

Get Book

Harmonic Analysis of Spherical Functions on Real Reductive Groups by Ramesh Gangolli,Veeravalli S. Varadarajan Pdf

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 : V.S. Varadarajan
Publisher : Springer
Page : 531 pages
File Size : 40,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540374206

Get Book

Harmonic Analysis on Real Reductive Groups by V.S. Varadarajan Pdf

Author : W. Barker,P. Sally
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461204558

Get Book

Harmonic Analysis on Reductive Groups by W. Barker,P. Sally Pdf

A conference on Harmonic Analysis on Reductive Groups was held at Bowdoin College in Brunswick, Maine from July 31 to August 11, 1989. The stated goal of the conference was to explore recent advances in harmonic analysis on both real and p-adic groups. It was the first conference since the AMS Summer Sym posium on Harmonic Analysis on Homogeneous Spaces, held at Williamstown, Massachusetts in 1972, to cover local harmonic analysis on reductive groups in such detail and to such an extent. While the Williamstown conference was longer (three weeks) and somewhat broader (nilpotent groups, solvable groups, as well as semisimple and reductive groups), the structure and timeliness of the two meetings was remarkably similar. The program of the Bowdoin Conference consisted of two parts. First, there were six major lecture series, each consisting of several talks addressing those topics in harmonic analysis on real and p-adic groups which were the focus of intensive research during the previous decade. These lectures began at an introductory level and advanced to the current state of research. Sec ond, there was a series of single lectures in which the speakers presented an overview of their latest research.

Author : B. Harish-Chandra
Publisher : Springer
Page : 135 pages
File Size : 42,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540363729

Get Book

Harmonic Analysis on Reductive p-adic Groups by B. Harish-Chandra Pdf

Author : Weng Lin
Publisher : World Scientific
Page : 556 pages
File Size : 46,8 Mb
Release : 2018-02-07
Category : Mathematics
ISBN : 9789813230668

Get Book

Zeta Functions Of Reductive Groups And Their Zeros by Weng Lin Pdf

This book provides a systematic account of several breakthroughs in the modern theory of zeta functions. It contains two different approaches to introduce and study genuine zeta functions for reductive groups (and their maximal parabolic subgroups) defined over number fields. Namely, the geometric one, built up from stability of principal lattices and an arithmetic cohomology theory, and the analytic one, from Langlands' theory of Eisenstein systems and some techniques used in trace formula, respectively. Apparently different, they are unified via a Lafforgue type relation between Arthur's analytic truncations and parabolic reductions of Harder–Narasimhan and Atiyah–Bott. Dominated by the stability condition and/or the Lie structures embedded in, these zeta functions have a standard form of the functional equation, admit much more refined symmetric structures, and most surprisingly, satisfy a weak Riemann hypothesis. In addition, two levels of the distributions for their zeros are exposed, i.e. a classical one giving the Dirac symbol, and a secondary one conjecturally related to GUE. This book is written not only for experts, but for graduate students as well. For example, it offers a summary of basic theories on Eisenstein series and stability of lattices and arithmetic principal torsors. The second part on rank two zeta functions can be used as an introduction course, containing a Siegel type treatment of cusps and fundamental domains, and an elementary approach to the trace formula involved. Being in the junctions of several branches and advanced topics of mathematics, these works are very complicated, the results are fundamental, and the theory exposes a fertile area for further research. Contents: Non-Abelian Zeta Functions Rank Two Zeta Functions Eisenstein Periods and Multiple L-Functions Zeta Functions for Reductive Groups Algebraic, Analytic Structures and Rieman Hypothesis Geometric Structures and Riemann Hypothesis Five Essays on Arithmetic Cohomology Readership: Graduate students and researchers in the theory of zeta functions. Keywords: Zeta Function;Riemann Hypothesis;Stability;Lattice;Fundamental Domain;Reductive Group;Root System;Eisenstein Series;Truncation;Arithmetic Principal Torsor;Adelic CohomologyReview: Key Features: Genuine zeta functions for reductive groups over number fields are introduced and studied systematically, based on (i) fine parabolic structures and Lie structures involved, (ii) a new stability theory for arithmetic principal torsors over number fields, and (iii) trace formula via a geometric understanding of Arthur's analytic truncations For the first time in history, we prove a weak Riemann hypothesis for zeta functions of reductive groups defined over number fields Not only the theory is explained, but the process of building the theory is elaborated in great detail

Author : Gerrit Heckman
Publisher : Academic Press
Page : 239 pages
File Size : 53,6 Mb
Release : 1995-02-08
Category : Mathematics
ISBN : 9780080533292

Get Book

Harmonic Analysis and Special Functions on Symmetric Spaces by Gerrit Heckman Pdf

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

Author : Ali Baklouti,Takaaki Nomura
Publisher : Springer Nature
Page : 217 pages
File Size : 46,8 Mb
Release : 2019-08-31
Category : Mathematics
ISBN : 9783030265625

Get Book

Geometric and Harmonic Analysis on Homogeneous Spaces by Ali Baklouti,Takaaki Nomura Pdf

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 : Alessandro Figa-Talamanca
Publisher : CRC Press
Page : 160 pages
File Size : 45,5 Mb
Release : 2020-11-25
Category : Mathematics
ISBN : 9781000116748

Get Book

Harmonic Analysis on Free Groups by Alessandro Figa-Talamanca Pdf

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.

Author : Jean-Philippe Anker,Bent Orsted
Publisher : Springer Science & Business Media
Page : 183 pages
File Size : 48,9 Mb
Release : 2006-02-25
Category : Mathematics
ISBN : 9780817644260

Get Book

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 : Calvin C. Moore
Publisher : American Mathematical Society(RI)
Page : 488 pages
File Size : 55,6 Mb
Release : 1973
Category : Mathematics
ISBN : STANFORD:36105031376473

Get Book

Harmonic Analysis on Homogeneous Spaces by Calvin C. Moore Pdf

Author : Audrey Terras
Publisher : Cambridge University Press
Page : 456 pages
File Size : 48,7 Mb
Release : 1999-03-28
Category : Mathematics
ISBN : 0521457181

Get Book

Fourier Analysis on Finite Groups and Applications by Audrey Terras Pdf

It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.

Author : Harish-Chandra,Robert S. Doran,V. S. Varadarajan
Publisher : American Mathematical Soc.
Page : 551 pages
File Size : 47,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821811979

Get Book

The Mathematical Legacy of Harish-Chandra by Harish-Chandra,Robert S. Doran,V. S. Varadarajan Pdf

Harish-Chandra was a mathematician of great power, vision, and remarkable ingenuity. His profound contributions to the representation theory of Lie groups, harmonic analysis, and related areas left researchers a rich legacy that continues today. This book presents the proceedings of an AMS Special Session entitled, ""Representation Theory and Noncommutative Harmonic Analysis: A Special Session Honoring the Memory of Harish-Chandra"", which marked 75 years since his birth and 15 years since his untimely death at age 60. Contributions to the volume were written by an outstanding group of internationally known mathematicians. Included are expository and historical surveys and original research papers.The book also includes talks given at the IAS Memorial Service in 1983 by colleagues who knew Harish-Chandra well. Also reprinted are two articles entitled, ""Some Recollections of Harish-Chandra"", by A. Borel, and ""Harish-Chandra's c-Function: A Mathematical Jewel"", by S. Helgason. In addition, an expository paper, ""An Elementary Introduction to Harish-Chandra's Work"", gives an overview of some of his most basic mathematical ideas with references for further study. This volume offers a comprehensive retrospective of Harish-Chandra's professional life and work. Personal recollections give the book particular significance. Readers should have an advanced-level background in the representation theory of Lie groups and harmonic analysis. For other wonderful titles written by this author see: ""Euler through Time: A New Look at Old Themes"", ""Supersymmetry for Mathematicians: An Introduction"", ""The Selected Works of V.S. Varadarajan"", and ""Algebra in Ancient and Modern Times"".

Author : Phillip Griffiths,Sigurdur Helgason
Publisher : American Mathematical Soc.
Page : 657 pages
File Size : 50,8 Mb
Release : 1989
Category : Education
ISBN : 9780821845301

Get Book

Geometric Analysis on Symmetric Spaces by Phillip Griffiths,Sigurdur Helgason Pdf

"This book gives the first systematic exposition of geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of Lie groups. The book starts with modern integral geometry for double fibrations and treats several examples in detail. After discussing the theory of Radon transforms and Fourier transforms on symmetric spaces, inversion formulas, and range theorems, Helgason examines applications to invariant differential equations on symmetric spaces, existence theorems, and explicit solution formulas, particularly potential theory and wave equations. The canonical multitemporal wave equation on a symmetric space is included. The book concludes with a chapter on eigenspace representations - that is, representations on solution spaces of invariant differential equations."--BOOK JACKET.

Author : Pascal Auscher,T. Coulhon,Alexander Grigoryan
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 54,5 Mb
Release : 2003
Category : Elliptic operators
ISBN : 9780821833834

Get Book

Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces by Pascal Auscher,T. Coulhon,Alexander Grigoryan Pdf

This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.

Author : Eric Grinberg,Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 249 pages
File Size : 41,7 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821851203

Get Book

Integral Geometry and Tomography by Eric Grinberg,Eric Todd Quinto Pdf

This book contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Integral Geometry and Tomography, held in June 1989 at Humboldt State University in Arcata, California. The papers collected here represent current research in these two interrelated fields. The articles in pure mathematics range over such diverse areas as combinatorics, geometric inequalities, micro-local analysis, group theory, and harmonic analysis. The interplay between Lie group theory, geometry, harmonic analysis, and Radon transforms is well covered.The papers on tomography reflect current research on X-ray computed tomography, as well as radiation dose planning, radar, and partial differential equations. In addition to describing current research, this book provides a useful perspective on the interplay between the fields. For example, abstract theorems about Radon transforms are used to understand applied mathematics, while applied mathematics motivates some of the results in pure mathematics. Though directed at specialists in the field, the book would also be of interest to others who wish to understand current research in these areas and to witness how they relate to other branches of mathematics.