UID:
almahu_9949697351902882
Format:
1 online resource (678 p.)
ISBN:
1-281-76359-4
,
9786611763596
,
0-08-087432-0
Series Statement:
Pure and applied mathematics (Academic Press) ; 113
Content:
Groups & Geometric Analysis
Note:
Description based upon print version of record.
,
Front Cover; Groups and Geometric Analysis: Integral Geometry, Invariant Differential Operators, and Spherical Functions; Copyright Page; Contents; Preface; Suggestions to the Reader; Tentative Contents of the Sequel; Introduction: Geometric Fourier Analysis on Spaces of Constant Curvature; 1. Harmonic Analysis on Homogeneous Spaces; 2. The Euclidean Plane R2; 3. The Sphere S2; 4. The Hyperbolic Plane H2; Chapter I. Integral Geometry and Radon Transforms; 1. Integration on Manifolds; 2. The Radon Transform on Rn
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3. A Duality in Integral Geometry. Generalized Radon Transforms and Orbital Integrals4. The Radon Transform on Two-Point Homogeneous Spaces. The X-Ray Transform; 5. Integral Formulas; 6. Orbital Integrals; Exercises and Further Results; Notes; Chapter II. Invariant Differential Operators; 1. Differentiable Functions on Rn; 2. Differential Operators on Manifolds; 3. Geometric Operations on Differential Operators; 4. Invariant Differential Operators on Lie Groups and Homogeneous Spaces; 5. Invariant Differential Operators on Symmetric Spaces; Exercises and Further Results; Notes
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Chapter III. Invariants and Harmonic Polynomials1. Decomposition of the Symmetric Algebra. Harmonic Polynomials; 2. Decomposition of the Exterior Algebra. Primitive Forms; 3. Invariants for the Weyl Group; 4. The Orbit Structure of p; 5. Harmonic Polynomials on p; Exercises and Further Results; Notes; Chapter IV. Spherical Functions and Spherical Transforms; 1. Representations; 2. Spherical Functions: Preliminaries; 3. Elementary Properties of Spherical Functions; 4. Integral Formulas for Spherical Functions. Connections with Representations; 5. Harish-Chandra's Spherical Function Expansion
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6. The c-Function7. The Paley-Wiener Theorem and the Inversion Formula for the Spherical Transform; 8. The Bounded Spherical Functions; 9. The Spherical Transform on p, the Euclidean Type; 10. Convexity Theorems; Exercises and Further Results; Notes; Chapter V. Analysis on Compact Symmetric Spaces; 1. Representations of Compact Lie Groups; 2. Fourier Expansions on Compact Groups; 3. Fourier Decomposition of a Representation; 4. The Case of a Compact Symmetric Space; Exercises and Further Results; Notes; Solutions to Exercises; Appendix; 1. The Finite-Dimensional Representations of sl(2, C)
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2. Representations and Reductive Lie Algebras3. Some Algebraic Tools; Bibliography; Symbols Frequently Used; Index
,
English
Additional Edition:
ISBN 0-12-338301-3
Language:
English
