Harmonic analysis on commutative spaces / Joseph A. Wolf.

Format:

Book

Author/Creator:

Wolf, Joseph Albert, 1936- author.

Series:

Mathematical surveys and monographs ; no. 142.

Mathematical surveys and monographs, 0076-5376 ; volume 142

Language:

English

Subjects (All):

Harmonic analysis.

Topological groups.

Abelian groups.

Algebraic spaces.

Geometry, Differential.

Physical Description:

1 online resource (408 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2007]

Language Note:

English

Summary:

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.

Contents:

""CONTENTS""; ""INTRODUCTION""; ""Acknowledgments""; ""Notational Conventions""; ""PART 1. GENERAL THEORY OF TOPOLOGICAL GROUPS""; ""Chapter 1. Basic Topological Group Theory""; ""1.1. Definition and Separation Properties""; ""1.2. Subgroups, Quotient Groups, and Quotient Spaces""; ""1.3. Connectedness""; ""1.4. Covering Groups""; ""1.5. Transformation Groups and Homogeneous Spaces""; ""1.6. The Locally Compact Case""; ""1.7. Product Groups""; ""1.8. Invariant Metrics on Topological Groups""; ""Chapter 2. Some Examples""; ""2.1. General and Special Linear Groups""; ""2.2. Linear Lie Groups""

""2.3. Groups Defined by Bilinear Forms""""2.4. Groups Defined by Hermitian Forms""; ""2.5. Degenerate Forms""; ""2.6. Automorphism Groups of Algebras""; ""2.7. Spheres, Projective Spaces and Grassmannians""; ""2.8. Complexification of Real Groups""; ""2.9. p�adic Groups""; ""2.10. Heisenberg Groups""; ""Chapter 3. Integration and Convolution""; ""3.1. Definition and Examples""; ""3.2. Existence and Uniqueness of Haar Measure""; ""3.3. The Modular Function""; ""3.4. Integration on Homogeneous Spaces""; ""3.5. Convolution and the Lebesgue Spaces""; ""3.6. The Group Algebra""

""4.6. Continuous Direct Sums of Representations""""4.7. Induced Representations""; ""4.8. Vector Bundle Interpretation""; ""4.9. Mackey's Little�Group Theorem""; ""4.9A. The Normal Subgroup Case""; ""4.9B. Cohomology and Projective Representations""; ""4.9C. Cocycle Representations and Extensions""; ""4.10. Mackey Theory and the Heisenberg Group""; ""Chapter 5. Representations of Compact Groups""; ""5.1. Finite Dimensionality""; ""5.2. Orthogonality Relations""; ""5.3. Characters and Projections""; ""5.4. The Peter�Weyl Theorem""; ""5.5. The Plancherel Formula""

""5.6. Decomposition into Irreducibles""""5.7. Some Basic Examples""; ""5.7A. The Group U(1)""; ""5.7B. The Group SU(2)""; ""5.7C. The Group SO(3)""; ""5.7D. The Group SO(4)""; ""5.7E. The Sphere S[sup(2)]""; ""5.7F. The Sphere S[sup(3)]""; ""5.8. Real, Complex and Quaternion Representations""; ""5.9. The Frobenius Reciprocity Theorem""; ""Chapter 6. Compact Lie Groups and Homogeneous Spaces""; ""6.1. Some Generalities on Lie Groups""; ""6.2. Reductive Lie Groups and Lie Algebras""; ""6.3. Cartan's Highest Weight Theory""; ""6.4. The Peter�Weyl Theorem and the Plancherel Formula""

""6.5. Complex Flag Manifolds and Holomorphic Vector Bundles""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 367-372) and indexes.

Description based on print version record.

ISBN:

1-4704-1369-8