Holomorphy and convexity in Lie theory

>> Google Books

所蔵情報QRコード

Holomorphy and convexity in Lie theory / by Karl-Hermann Neeb

資料種別:: 図書
出版情報:: Berlin : Walter de Gruyter, 2000, c1999
形態:: xxi, 778 p. ; 25 cm
シリーズ名:: De Gruyter expositions in mathematics ; v. 28 <BA10903360>
著者名:: Neeb, Karl-Hermann <DA06407645>
ISBN:: 9783110156690 [3110156695]
書誌ID:: BA4465909X

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references (p. [751]-766) and index

主題:

Convex functions; Lie groups; Representations of groups

言語:

英語

目次情報:

Preface

Introduction

Abstract Representation Theory / A.：

Reproducing Kernel Spaces / Chapter I.：

Operator-Valued Positive Definite Kernels / I.1.：

The Cone of Positive Definite Kernels / I.2.：

Representations of Involutive Semigroups / Chapter II.：

Involutive Semigroups / II.1.：

Bounded Representations / II.2.：

Hermitian Representations / II.3.：

Representations on Reproducing Kernel Spaces / II.4.：

Positive Definite Functions on Involutive Semigroups / Chapter III.：

Positive Definite Functions--the Discrete Case / III.1.：

Enveloping C*-algebras / III.2.：

Multiplicity Free Representations / III.3.：

Continuous and Holomorphic Representations / Chapter IV.：

Continuous Representations and Positive Definite Functions / IV.1.：

Holomorphic Representations of Involutive Semigroups / IV.2.：

Convex Geometry and Representations of Vector Spaces / B.：

Convex Sets and Convex Functions / Chapter V.：

Convex Sets and Cones / V.1.：

Finite Reflection Groups and Convex Sets / V.2.：

Convex Functions and Fenchel Duality / V.3.：

Laplace Transforms / V.4.：

The Characteristic Function of a Convex Set / V.5.：

Representations of Cones and Tubes / Chapter VI.：

Commutative Representation Theory / VI.1.：

Representations of Cones / VI.2.：

Holomorphic Representations of Tubes / VI.3.：

Realization of Cyclic Representations by Holomorphic Functions / VI.4.：

Holomorphic Extensions of Unitary Representations / VI.5.：

Convex Geometry of Lie Algebras / C.：

Convexity in Lie Algebras / Chapter VII.：

Compactly Embedded Cartan Subalgebras / VII.1.：

Root Decompositions / VII.2.：

Lie Algebras With Many Invariant Convex Sets / VII.3.：

Convexity Theorems and Their Applications / Chapter VIII.：

Admissible Coadjoint Orbits and Convexity Theorems / VIII.1.：

The Structure of Admissible Lie Algebras / VIII.2.：

Invariant Elliptic Cones in Lie Algebras / VIII.3.：

Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups / D.：

Unitary Highest Weight Representations: Algebraic Theory / Chapter IX.：

Generalized Highest Weight Representations / IX.1.：

Positive Complex Polarizations / IX.2.：

Highest Weight Modules of Finite-Dimensional Lie Algebras / IX.3.：

The Metaplectic Factorization / IX.4.：

Unitary Highest Weight Representations of Hermitian Lie Algebras / IX.5.：

Unitary Highest Weight Representations: Analytic Theory / Chapter X.：

The Convex Moment Set of a Unitary Representation / X.1.：

Irreducible Unitary Representations / X.2.：

The Metaplectic Representation and Its Applications / X.3.：

Special Properties of Unitary Highest Weight Representations / X.4.：

Moment Sets for C*-algebras / X.5.：

Moment Sets for Group Representations / X.6.：

Complex Ol'shanskii Semigroups and Their Representations / Chapter XI.：

Lawson's Theorem on Ol'shanskii Semigroups / XI.1.：

Holomorphic Extension of Unitary Representations / XI.2.：

Holomorphic Representations of Ol'shanskii Semigroups / XI.3.：

Irreducible Holomorphic Representations / XI.4.：

Gelfand-Raikov Theorems for Ol'shanskii Semigroups / XI.5.：

Decomposition and Characters of Holomorphic Representations / XI.6.：

Realization of Highest Weight Representations on Complex Domains / Chapter XII.：

The Structure of Groups of Harish-Chandra Type / XII.1.：

Representations of Groups of Harish-Chandra Type / XII.2.：

The Compression Semigroup and Its Representations / XII.3.：

Examples / XII.4.：

Hilbert Spaces of Square Integrable Holomorphic Functions / XII.5.：

Complex Geometry and Representation Theory / E.：

Complex and Convex Geometry of Complex Semigroups / Chapter XIII.：

Locally Convex Functions and Local Recession Cones / XIII.1.：

Invariant Convex Sets and Functions in Lie Algebras / XIII.2.：

Calculations in Low-Dimensional Cases / XIII.3.：

Biinvariant Plurisubharmonic Functions / XIII.4.：

Complex Semigroups and Stein Manifolds / XIII.5.：

Biinvariant Domains of Holomorphy / XIII.6.：

Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups / Chapter XIV.：

Biinvariant Hilbert Spaces / XIV.1.：

Hardy Spaces Defined by Sup-Norms / XIV.2.：

Hardy Spaces Defined by Square Integrability / XIV.3.：

The Fine Structure of Hardy Spaces / XIV.4.：

Coherent State Representations / Chapter XV.：

Complex Structures on Homogeneous Spaces / XV.1.：

Heisenberg's Uncertainty Principle and Coherent States / XV.2.：

Appendices

Bounded Operators on Hilbert Spaces / Appendix I.：

Spectral Measures and Unbounded Operators / Appendix II.：

Holomorphic Functions on Infinite-Dimensional Spaces / Appendix III.：

Symplectic Geometry / Appendix IV.：

Simple Modules of p-Length 2 / Appendix V.：

Symplectic Modules of Convex Type / Appendix VI.：

Square Integrable Representations of Locally Compact Groups / Appendix VII.：

The Stone-von Neumann-Mackey Theorem / Appendix VIII.：

Bibliography

List of Symbols

Index

Preface

Introduction

Abstract Representation Theory / A.：

Reproducing Kernel Spaces / Chapter I.：

Operator-Valued Positive Definite Kernels / I.1.：

The Cone of Positive Definite Kernels / I.2.：

続きを見る

東工大ブックレビュー

類似資料:

1 図書 Lie semigroups and their applications (: gw ; : us) Hilgert, Joachim, Neeb, Karl-Hermann Springer-Verlag	7 図書 Lie groups, Lie algebras, and representations : an elementary introduction Hall, Brian C. Springer
2 図書 Unitary representation theory of exponential Lie groups Leptin, Horst, 1927-, Ludwig, Jean, 1947- W. de Gruyter	8 図書 Lectures on Lie groups (: pbk ; : cloth) Adams, J. Frank (John Frank) W.A. Benjamin
3 電子ブック Developments and Trends in Infinite-Dimensional Lie Theory Karl-Hermann Neeb, Arturo Pianzola, Neeb, Karl-Hermann, Pianzola, Arturo SpringerLink Books - AutoHoldings, Birkhäuser Boston	9 図書 Characters of connected Lie groups Pukanszky, L American Mathematical Society
4 図書 Lie-Cartan-Ehresmann theory Hermann, Robert, 1931- Math Sci Press	10 図書 Lie groups beyond an introduction (: us ; : gw) Knapp, Anthony W. Birkhäuser
5 図書 Physical aspects of Lie group theory Hermann, Robert, 1931- Presses de l'Université de Montréal	11 図書 Loops in group theory and lie theory Nagy, Péter Tibor, Strambach, Karl Walter de Gruyter
6 図書 Lie groups, Lie algebras, and their representations Varadarajan, V. S. Prentice-Hall	12 電子ブック Structure and Geometry of Lie Groups Hilgert, Joachim, Neeb, Karl-Hermann SpringerLink Books - AutoHoldings, Springer New York