Harmonic analysis on semi-simple Lie groups

著者

• Warner, Garth

書誌事項

Harmonic analysis on semi-simple Lie groups

Garth Warner

（Die Grundlehren der mathematischen Wissenschaften, Bd. 188-189）

Springer-Verlag, 1972

• v. 1 : gw
• v. 1 : us
• v. 1 : pbk
• v. 2 : gw
• v. 2 : us
• v. 2 : pbk

注記

Bibliography: v. 1, p. [500]-523; v. 2, p. [460]-483

Includes indexes

内容説明・目次

巻冊次

v. 1 : gw ISBN 9783540054689

内容説明

The representation theory of locally compact groups has been vig- orously developed in the past twenty-five years or so; of the various branches of this theory, one of the most attractive (and formidable) is the representation theory of semi-simple Lie groups which, to a great extent, is the creation of a single man: Harish-Chandra. The chief objective of the present volume and its immediate successor is to provide a reasonably self-contained introduction to Harish-Chandra's theory. Granting cer- tain basic prerequisites (cf. infra), we have made an effort to give full details and complete proofs of the theorems on which the theory rests. The structure of this volume and its successor is as follows. Each book is divided into chapters; each chapter is divided into sections; each section into numbers. We then use the decimal system of reference; for example, 1. 3. 2 refers to the second number in the third section of the first chapter. Theorems, Propositions, Lemmas, and Corollaries are listed consecutively throughout any given number. Numbers which are set in fine print may be omitted at a first reading. There are a variety of Exam- ples scattered throughout the text; the reader, if he is so inclined, can view them as exercises ad libitum. The Appendices to the text collect certain ancillary results which will be used on and off in the systematic exposi- tion; a reference of the form A2.

目次

1 The Structure of Real Semi-Simple Lie Groups.- 1.1 Preliminaries.- 1.1.1 The Structure of Complex Semi-Simple Lie Algebras.- 1.1.2 Root Systems I - Basic Properties.- 1.1.3 Root Systems II -?-Systems.- 1.1.4 Structure of the Nilpotent Constituent in an Iwasawa Decomposition.- 1.1.5 Reductive Lie Algebras and Groups.- 1.2 The Bruhat Decomposition-Parabolic Subgroups.- 1.2.1 Tits Systems.- 1.2.2 The Complex Case.- 1.2.3 Boundary Subgroups and Parabolic Subgroups of a Real Semi-Simple Lie Group.- 1.2.4 Levi Subgroups of a Parabolic Subgroup. The Langlands Decomposition.- 1.3 Cartan Subalgebras.- 1.3.1 Conjugacy of Cartan Subalgebras in a Real Reductive Lie Algebra.- 1.3.2 Classification of Roots.- 1.3.3 Fundamental Cartan Subalgebras.- 1.3.4 Regular and Semi-Regular Elements in a Reductive Lie Algebra.- 1.3.5 Semi-Simple and Nilpotent Elements in a Reductive Lie Algebra.- 1.4 Cartan Subgroups.- 1.4.1 Structure Theorems.- 1.4.2 The Groups W(G,J) and W(G,J0).- 1.4.3 Semi-Simple and Unipotent Elements in a Reductive Lie Group.- 2 The Universal Enveloping Algebra of a Semi-Simple Lie Algebra.- 2.1 Invariant Theory I - Generalities.- 2.1.1 Modules.- 2.1.2 The Fundamental Theorem of Invariant Theory.- 2.1.3 Invariants of Finite Groups Generated by Reflections.- 2.1.4 Symmetric Algebras and Formal Power Series.- 2.1.5 Weyl Group Invariants.- 2.2 Invariant Theory II - Applications to Reductive Lie Algebras.- 2.2.1 A Theorem of Harish-Chandra.- 2.2.2 Theorems of Finitude.- 2.3 On the Structure of the Universal Enveloping Algebra.- 2.3.1 Generalities.- 2.3.2 Existence of Sufficiently Many Finite Dimensional Representations.- 2.3.3 The Reductive Case.- 2.4 Representations of a Reductive Lie Algebra.- 2.4.1 Simple Modules - The Theorem of Highest Weight.- 2.4.2 The Formula of H. Weyl and B. Kostant.- 2.4.3 The Characters of a Reductive Lie Algebra.- 2.5 Representations on Cohomology Groups.- 2.5.1 The Riemann-Roch Theorem for Lie Algebras.- 2.5.2 Theorems of Bott and Kostant.- 3 Finite Dimensional Representations of a Semi-Simple Lie Group.- 3.1 Holomorphic Representations of a Complex Semi-Simple Lie Group.- 3.1.1 Generalities.- 3.1.2 The Borel-Weil Theorem.- 3.2 Unitary Representations of a Compact Semi-Simple Lie Group.- 3.2.1 The Invariant Integral on a Compact Semi-Simple Lie Algebra.- 3.2.2 The Planche rel Theorem for a Compact Connected Semi-Simple Lie Group.- 3.3 Finite Dimensional Class One Representations of a Real Semi-Simple Lie Group.- 3.3.1 The Theorem of E. Cartan and S. Helgason.- 3.3.2 Inequalities.- 4 Infinite Dimensional Group Representation Theory.- 4.1 Representations on a Locally Convex Space.- 4.1.1 Basic Concepts.- 4.1.2 Operations on Representations.- 4.1.3 Intertwining Forms and Operators.- 4.2 Representations on a Banach Space.- 4.2.1 Banach Representations of Associative Algebras.- 4.2.2 Banach Representations of Groups.- 4.3 Representations on a Hubert Space.- 4.3.1 Generalities.- 4.3.2 Examples.- 4.4 Differentiable Vectors, Analytic Vectors.- 4.4.1 Passage to U?.- 4.4.2 Absolute Convergence of the Fourier Series.- 4.4.3 A Density Theorem. Fourier Series in Function Spaces.- 4.4.4 Elliptic Elements in the Enveloping Algebra.- 4.4.5 Density of Analytic Vectors - The Theorem of Nelson.- 4.4.6 Analytic Domination - Applications to Representation Theory.- 4.4.7 The Paley-Wiener Space.- 4.5 Large Compact Subgroups.- 4.5.1 The Algebras Cc,?(G), Ic,?,(G).- 4.5.2 Groups with Large Compact Subgroups.- 4.5.3 Properties of Largeness.- 4.5.4 Naimark Equivalence.- 4.5.5 Infinitesimal Equivalence.- 4.5.6 Jordan-Holder Series - Multiplicities.- 4.5.7 Theorems of Finitude.- 4.5.8 Characters.- 4.5.9 Square Integrable Representations.- 5 Induced Representations.- 5.1 Unitarily Induced Representations.- 5.1.1 The Definition.- 5.1.2 Unitarily Induced Representations and Measures of Positive Type.- 5.1.3 Elementary Properties of Unitarily Induced Representations.- 5.2 Quasi-Invariant Distributions.- 5.2.1 The Global Situation.- 5.2.2 The Local Situation.- 5.2.3 A Fundamental Estimate.- 5.2.4 The Case of Countably Many Orbits.- 5.3 Irreducibility of Unitarily Induced Representations.- 5.3.1 On the Notion of Induced Representation.- 5.3.2 Estimation of the Intertwining Number.- 5.3.3 Reciprocity Theorems.- 5.3.4 Decomposition Theorems.- 5.4 Systems of Imprimitivity.- 5.4.1 Mackey's Orbital Analysis.- 5.4.2 Examples.- 5.5 Applications to Semi-Simple Lie Groups.- 5.5.1 The Subquotient Theorem.- 5.5.2 Irreducibility of the Principal P-Series - P Minimal.- 5.5.3 The Characters of the Principal P-Series - P Minimal.- 5.5.4 The Riemann-Lebesgue Lemma for the Principal P-Series - P Minimal.- Appendices.- 1 Quasi-Invariant Measures.- 2 Distributions on a Manifold.- 2.1 Differential Operators and Function Spaces.- 2.2 Tensor Products of Topological Vector Spaces.- 2.3 Vector Distributions.- 2.4 Distributions on a Lie Group.- General Notational Conventions.- List of Notations.- Guide to the Literature.

巻冊次

v. 2 : gw ISBN 9783540054696

目次

6 Spherical Functions - The General Theory.- 6.1 Fundamentals.- 6.1.1 Spherical Functions - Functional Properties.- 6.1.2 Spherical Functions - Differential Properties.- 6.2 Examples.- 6.2.1 Spherical Functions on Motion Groups.- 6.2.2 Spherical Functions on Semi-Simple Lie Groups.- 7 Topology on the Dual Plancherel Measure Introduction.- 7.1 Topology on the Dual.- 7.1.1 Generalities.- 7.1.2 Applications to Semi-Simple Lie Groups.- 7.2 Plancherel Measure.- 7.2.1 Generalities.- 7.2.2 The Plancherel Theorem for Complex Connected Semi-Simple Lie Groups.- 8 Analysis on a Semi-Simple Lie Group.- 8.1 Preliminaries.- 8.1.1 Acceptable Groups.- 8.1.2 Normalization of Invariant Measures.- 8.1.3 Integration Formulas.- 8.1.4 A Theorem of Compacity.- 8.1.5 The Standard Semi-Norm on a Semi-Simple Lie Group.- 8.1.6 Completely Invariant Sets.- 8.2 Differential Operators on Reductive Lie Groups and Algebras.- 8.2.1 Radial Components of Differential Operators on a Manifold.- 8.2.2 Radial Components of Polynomial Differential Operators on a Reductive Lie Algebra.- 8.2.3 Radial Components of Left Invariant Differential Operators on a Reductive Lie Group.- 8.2.4 The Connection between Differential Operators in the Algebra and on the Group.- 8.3 Central Eigendistributions on Reductive Lie Algebras and Groups.- 8.3.1 The Main Theorem in the Algebra.- 8.3.2 Properties of FT-I.- 8.3.3 The Main Theorem on the Group.- 8.3.4 Properties of FT- II.- 8.3.5 Rapidly Decreasing Functions on a Euclidean Space.- 8.3.6 Tempered Distributions on a Reductive Lie Algebra.- 8.3.7 Rapidly Decreasing Functions on a Reductive Lie Group.- 8.3.8 Tempered Distributions on a Reductive Lie Group.- 8.3.9 Tools for Harmonic Analysis on G.- 8.4 The Invariant Integral on a Reductive Lie Algebra.- 8.4.1 The Invariant Integral - Definition and Properties.- 8.4.2 Computations in sl(2, R).- 8.4.3 Continuity of the Map f ? ? f.- 8.4.4 Extension Problems.- 8.4.5 The Main Theorem.- 8.5 The Invariant Integral on a Reductive Lie Group.- 8.5.1 The Invariant Integral - Definition and Properties.- 8.5.2 The Inequalities of Descent.- 8.5.3 The Transformations of Descent.- 8.5.4 The Invariant Integral and the Transformations of Descent.- 8.5.5 Estimation of ?f and its Derivatives.- 8.5.6 An Important Inequality.- 8.5.7 Convergence of Certain Integrals.- 8.5.8 Continuity of the Map f? ?f.- 9 Spherical Functions on a Semi-Simple Lie Group.- 9.1 Asymptotic Behavior of ?-Spherical Functions on a Semi-Simple Lie Group.- 9.1.1 The Main Results.- 9.1.2 Analysis in the Universal Enveloping Algebra.- 9.1.3 The Space S(?,?).- 9.1.4 The Rational Functions ??.- 9.1.5 The Expansion of ?-Spherical Functions.- 9.1.6 Investigation of the c-Function.- 9.1.7 Applications to Zonal Spherical Functions.- 9.2 Zonal Spherical Functions on a Semi-Simple Lie Group.- 9.2.1 Statement of Results - Immediate Applications.- 9.2.2 The Plancherel Theorem for I2(G).- 9.2.3 The Paley-Wiener Theorem for I2(G).- 9.2.4 Harmonic Analysis in I1(G).- 9.3 Spherical Functions and Differential Equations.- 9.3.1 The Weak Inequality and Some of its Implications.- 9.3.2 Existence and Uniqueness of the Indices I.- 9.3.3 Existence and Uniqueness of the Indices II.- 10 The Discrete Series for a Semi-Simple Lie Group - Existence and Exhaustion.- 10.1 The Role of the Distributions ?? in the Harmonic Analysis on G.- 10.1.1 Existence and Uniqueness of the ??.- 10.1.2 Expansion of Z-Finite Functions in C-(G).- 10.2 Theory of the Discrete Series.- 10.2.1 Existence of the Discrete Series.- 10.2.2 The Characters of the Discrete Series I - Implication of the Orthogonality Relations.- 10.2.3 The Characters of the Discrete Series II - Application of the Differential Equations.- 10.2.4 The Theorem of Harish-Chandra.- Epilogue.- Append.- 3 Some Results on Differential Equations.- 3.1 The Main Theorems.- 3.2 Lemmas from Analysis.- 3.3 Analytic Continuation of Solutions.- 3.4 Decent Convergence.- 3.5 Normal Sequences of is-Polynomials.- General Notational Conventions.- List of Notations.- Guide to the Literature.- Subject Index to Volumes I and II.

巻冊次

v. 1 : pbk ISBN 9783642502774

内容説明

The representation theory of locally compact groups has been vig orously developed in the past twenty-five years or so; of the various branches of this theory, one of the most attractive (and formidable) is the representation theory of semi-simple Lie groups which, to a great extent, is the creation of a single man: Harish-Chandra. The chief objective of the present volume and its immediate successor is to provide a reasonably self-contained introduction to Harish-Chandra's theory. Granting cer tain basic prerequisites (cf. infra), we have made an effort to give full details and complete proofs of the theorems on which the theory rests. The structure of this volume and its successor is as follows. Each book is divided into chapters; each chapter is divided into sections; each section into numbers. We then use the decimal system of reference; for example, 1. 3. 2 refers to the second number in the third section of the first chapter. Theorems, Propositions, Lemmas, and Corollaries are listed consecutively throughout any given number. Numbers which are set in fine print may be omitted at a first reading. There are a variety of Exam ples scattered throughout the text; the reader, if he is so inclined, can view them as exercises ad libitum. The Appendices to the text collect certain ancillary results which will be used on and off in the systematic exposi tion; a reference of the form A2.

目次

1 The Structure of Real Semi-Simple Lie Groups.- 1.1 Preliminaries.- 1.1.1 The Structure of Complex Semi-Simple Lie Algebras.- 1.1.2 Root Systems I - Basic Properties.- 1.1.3 Root Systems II -?-Systems.- 1.1.4 Structure of the Nilpotent Constituent in an Iwasawa Decomposition.- 1.1.5 Reductive Lie Algebras and Groups.- 1.2 The Bruhat Decomposition-Parabolic Subgroups.- 1.2.1 Tits Systems.- 1.2.2 The Complex Case.- 1.2.3 Boundary Subgroups and Parabolic Subgroups of a Real Semi-Simple Lie Group.- 1.2.4 Levi Subgroups of a Parabolic Subgroup. The Langlands Decomposition.- 1.3 Cartan Subalgebras.- 1.3.1 Conjugacy of Cartan Subalgebras in a Real Reductive Lie Algebra.- 1.3.2 Classification of Roots.- 1.3.3 Fundamental Cartan Subalgebras.- 1.3.4 Regular and Semi-Regular Elements in a Reductive Lie Algebra.- 1.3.5 Semi-Simple and Nilpotent Elements in a Reductive Lie Algebra.- 1.4 Cartan Subgroups.- 1.4.1 Structure Theorems.- 1.4.2 The Groups W(G,J) and W(G,J0).- 1.4.3 Semi-Simple and Unipotent Elements in a Reductive Lie Group.- 2 The Universal Enveloping Algebra of a Semi-Simple Lie Algebra.- 2.1 Invariant Theory I - Generalities.- 2.1.1 Modules.- 2.1.2 The Fundamental Theorem of Invariant Theory.- 2.1.3 Invariants of Finite Groups Generated by Reflections.- 2.1.4 Symmetric Algebras and Formal Power Series.- 2.1.5 Weyl Group Invariants.- 2.2 Invariant Theory II - Applications to Reductive Lie Algebras.- 2.2.1 A Theorem of Harish-Chandra.- 2.2.2 Theorems of Finitude.- 2.3 On the Structure of the Universal Enveloping Algebra.- 2.3.1 Generalities.- 2.3.2 Existence of Sufficiently Many Finite Dimensional Representations.- 2.3.3 The Reductive Case.- 2.4 Representations of a Reductive Lie Algebra.- 2.4.1 Simple Modules - The Theorem of Highest Weight.- 2.4.2 The Formula of H. Weyl and B. Kostant.- 2.4.3 The Characters of a Reductive Lie Algebra.- 2.5 Representations on Cohomology Groups.- 2.5.1 The Riemann-Roch Theorem for Lie Algebras.- 2.5.2 Theorems of Bott and Kostant.- 3 Finite Dimensional Representations of a Semi-Simple Lie Group.- 3.1 Holomorphic Representations of a Complex Semi-Simple Lie Group.- 3.1.1 Generalities.- 3.1.2 The Borel-Weil Theorem.- 3.2 Unitary Representations of a Compact Semi-Simple Lie Group.- 3.2.1 The Invariant Integral on a Compact Semi-Simple Lie Algebra.- 3.2.2 The Planche rel Theorem for a Compact Connected Semi-Simple Lie Group.- 3.3 Finite Dimensional Class One Representations of a Real Semi-Simple Lie Group.- 3.3.1 The Theorem of E. Cartan and S. Helgason.- 3.3.2 Inequalities.- 4 Infinite Dimensional Group Representation Theory.- 4.1 Representations on a Locally Convex Space.- 4.1.1 Basic Concepts.- 4.1.2 Operations on Representations.- 4.1.3 Intertwining Forms and Operators.- 4.2 Representations on a Banach Space.- 4.2.1 Banach Representations of Associative Algebras.- 4.2.2 Banach Representations of Groups.- 4.3 Representations on a Hubert Space.- 4.3.1 Generalities.- 4.3.2 Examples.- 4.4 Differentiable Vectors, Analytic Vectors.- 4.4.1 Passage to U?.- 4.4.2 Absolute Convergence of the Fourier Series.- 4.4.3 A Density Theorem. Fourier Series in Function Spaces.- 4.4.4 Elliptic Elements in the Enveloping Algebra.- 4.4.5 Density of Analytic Vectors - The Theorem of Nelson.- 4.4.6 Analytic Domination - Applications to Representation Theory.- 4.4.7 The Paley-Wiener Space.- 4.5 Large Compact Subgroups.- 4.5.1 The Algebras Cc,?(G), Ic,?,(G).- 4.5.2 Groups with Large Compact Subgroups.- 4.5.3 Properties of Largeness.- 4.5.4 Naimark Equivalence.- 4.5.5 Infinitesimal Equivalence.- 4.5.6 Jordan-Hoelder Series - Multiplicities.- 4.5.7 Theorems of Finitude.- 4.5.8 Characters.- 4.5.9 Square Integrable Representations.- 5 Induced Representations.- 5.1 Unitarily Induced Representations.- 5.1.1 The Definition.- 5.1.2 Unitarily Induced Representations and Measures of Positive Type.- 5.1.3 Elementary Properties of Unitarily Induced Representations.- 5.2 Quasi-Invariant Distributions.- 5.2.1 The Global Situation.- 5.2.2 The Local Situation.- 5.2.3 A Fundamental Estimate.- 5.2.4 The Case of Countably Many Orbits.- 5.3 Irreducibility of Unitarily Induced Representations.- 5.3.1 On the Notion of Induced Representation.- 5.3.2 Estimation of the Intertwining Number.- 5.3.3 Reciprocity Theorems.- 5.3.4 Decomposition Theorems.- 5.4 Systems of Imprimitivity.- 5.4.1 Mackey's Orbital Analysis.- 5.4.2 Examples.- 5.5 Applications to Semi-Simple Lie Groups.- 5.5.1 The Subquotient Theorem.- 5.5.2 Irreducibility of the Principal P-Series - P Minimal.- 5.5.3 The Characters of the Principal P-Series - P Minimal.- 5.5.4 The Riemann-Lebesgue Lemma for the Principal P-Series - P Minimal.- Appendices.- 1 Quasi-Invariant Measures.- 2 Distributions on a Manifold.- 2.1 Differential Operators and Function Spaces.- 2.2 Tensor Products of Topological Vector Spaces.- 2.3 Vector Distributions.- 2.4 Distributions on a Lie Group.- General Notational Conventions.- List of Notations.- Guide to the Literature.

巻冊次

v. 2 : pbk ISBN 9783642516429

目次

6 Spherical Functions - The General Theory.- 6.1 Fundamentals.- 6.1.1 Spherical Functions - Functional Properties.- 6.1.2 Spherical Functions - Differential Properties.- 6.2 Examples.- 6.2.1 Spherical Functions on Motion Groups.- 6.2.2 Spherical Functions on Semi-Simple Lie Groups.- 7 Topology on the Dual Plancherel Measure Introduction.- 7.1 Topology on the Dual.- 7.1.1 Generalities.- 7.1.2 Applications to Semi-Simple Lie Groups.- 7.2 Plancherel Measure.- 7.2.1 Generalities.- 7.2.2 The Plancherel Theorem for Complex Connected Semi-Simple Lie Groups.- 8 Analysis on a Semi-Simple Lie Group.- 8.1 Preliminaries.- 8.1.1 Acceptable Groups.- 8.1.2 Normalization of Invariant Measures.- 8.1.3 Integration Formulas.- 8.1.4 A Theorem of Compacity.- 8.1.5 The Standard Semi-Norm on a Semi-Simple Lie Group.- 8.1.6 Completely Invariant Sets.- 8.2 Differential Operators on Reductive Lie Groups and Algebras.- 8.2.1 Radial Components of Differential Operators on a Manifold.- 8.2.2 Radial Components of Polynomial Differential Operators on a Reductive Lie Algebra.- 8.2.3 Radial Components of Left Invariant Differential Operators on a Reductive Lie Group.- 8.2.4 The Connection between Differential Operators in the Algebra and on the Group.- 8.3 Central Eigendistributions on Reductive Lie Algebras and Groups.- 8.3.1 The Main Theorem in the Algebra.- 8.3.2 Properties of FT-I.- 8.3.3 The Main Theorem on the Group.- 8.3.4 Properties of FT- II.- 8.3.5 Rapidly Decreasing Functions on a Euclidean Space.- 8.3.6 Tempered Distributions on a Reductive Lie Algebra.- 8.3.7 Rapidly Decreasing Functions on a Reductive Lie Group.- 8.3.8 Tempered Distributions on a Reductive Lie Group.- 8.3.9 Tools for Harmonic Analysis on G.- 8.4 The Invariant Integral on a Reductive Lie Algebra.- 8.4.1 The Invariant Integral - Definition and Properties.- 8.4.2 Computations in sl(2, R).- 8.4.3 Continuity of the Map f ? ? f.- 8.4.4 Extension Problems.- 8.4.5 The Main Theorem.- 8.5 The Invariant Integral on a Reductive Lie Group.- 8.5.1 The Invariant Integral - Definition and Properties.- 8.5.2 The Inequalities of Descent.- 8.5.3 The Transformations of Descent.- 8.5.4 The Invariant Integral and the Transformations of Descent.- 8.5.5 Estimation of ?f and its Derivatives.- 8.5.6 An Important Inequality.- 8.5.7 Convergence of Certain Integrals.- 8.5.8 Continuity of the Map f? ?f.- 9 Spherical Functions on a Semi-Simple Lie Group.- 9.1 Asymptotic Behavior of ?-Spherical Functions on a Semi-Simple Lie Group.- 9.1.1 The Main Results.- 9.1.2 Analysis in the Universal Enveloping Algebra.- 9.1.3 The Space S(?,?).- 9.1.4 The Rational Functions ??.- 9.1.5 The Expansion of ?-Spherical Functions.- 9.1.6 Investigation of the c-Function.- 9.1.7 Applications to Zonal Spherical Functions.- 9.2 Zonal Spherical Functions on a Semi-Simple Lie Group.- 9.2.1 Statement of Results - Immediate Applications.- 9.2.2 The Plancherel Theorem for I2(G).- 9.2.3 The Paley-Wiener Theorem for I2(G).- 9.2.4 Harmonic Analysis in I1(G).- 9.3 Spherical Functions and Differential Equations.- 9.3.1 The Weak Inequality and Some of its Implications.- 9.3.2 Existence and Uniqueness of the Indices I.- 9.3.3 Existence and Uniqueness of the Indices II.- 10 The Discrete Series for a Semi-Simple Lie Group - Existence and Exhaustion.- 10.1 The Role of the Distributions ?? in the Harmonic Analysis on G.- 10.1.1 Existence and Uniqueness of the ??.- 10.1.2 Expansion of Z-Finite Functions in C-(G).- 10.2 Theory of the Discrete Series.- 10.2.1 Existence of the Discrete Series.- 10.2.2 The Characters of the Discrete Series I - Implication of the Orthogonality Relations.- 10.2.3 The Characters of the Discrete Series II - Application of the Differential Equations.- 10.2.4 The Theorem of Harish-Chandra.- Epilogue.- Append.- 3 Some Results on Differential Equations.- 3.1 The Main Theorems.- 3.2 Lemmas from Analysis.- 3.3 Analytic Continuation of Solutions.- 3.4 Decent Convergence.- 3.5 Normal Sequences of is-Polynomials.- General Notational Conventions.- List of Notations.- Guide to the Literature.- Subject Index to Volumes I and II.

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詳細情報

• NII書誌ID(NCID): BA03959751
• ISBN:
  • 3540054685
  • 0387054685
  • 9783642502774
  • 3540054693
  • 0387054693
  • 9783642516429
• 出版国コード: gw
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Berlin ; New York
• ページ数/冊数: 2 v.
• 大きさ: 24 cm
• 分類:
  • LCC : QA387
  • DC : 512/.55
• 件名:
  • LCSH : Semisimple Lie groups
  • LCSH : Representations of groups
  • LCSH : Harmonic analysis
• 親書誌ID:
  • BA00007422