تحلیل هارمونیک و توابع خاص در فضاهای متقارن (چشم‌اندازهایی در ریاضیات)

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 This Sharply Focused Book Treats The Large Class Of Hypergeometric Functions Used In The Solution Of Differential Equations And In Physics. Although Known From The Time Of Euler, These Functions Can Now Be Understood For The First Time In The Context Of Harmonic Analysis And Symmetric Spaces. Divided Into Two Parts, The Material In Harmonic Analysis And Special Functions On Symmetric Spaces Is Based On Lectures Given For The European School Of Group Theory, An Advanced Course On Current 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 With Time-saving Examples. An Extensive Set Of Notes Supplements The Text. The Book Leads Readers From The Fundamentals Of Semisimple Symmetric Spaces To The Reimannian Case. The 19th Century Work Of Euler, Gauss, Kummer, Riemann, And Klein On Hypergeometric Functions Is Linked To Root Systems And Symmetric Spaces. Algebraic And Analytic Methods Are Used, With Many Connections Made In The Geometric Context Of Symmetric Spaces. This Volume Will Interest Harmonic Analysts, Those Working On Or Applying The Theory Of Symmetric Spaces, And Those With An Interest In Special Functions. Pt. I. Hypergeometric And Spherical Functions / G. Heckman -- Pt. Ii. Harmonic Analysis On Semisimple Symmetric Spaces / H. Schlichtkrull -- Pt. Iii. Are K-invariant Eisenstein Integrals For G/h Hypergeometric Functions? / G. Heckman. Gerrit Heckman, Henrik Schlicktkrull. Includes Bibliographical References And Index. Front Cover......Page 1 Harmonic Analysis and Special Functions on Symmetric Spaces......Page 4 Copyright Page......Page 5 Contents......Page 8 Preface......Page 10 Part I: Hypergeometric and Spherical Functions......Page 14 Part II: Harmonic Analysis on Semisimple Symmetric Spaces......Page 104 Part III: Are K-invariant Eisenstein Integrals for G / H Hypergeometric Functions?......Page 202 References......Page 222 Index......Page 236