This self-contained text concentrates on the perspective of analysis, assuming only elementary knowledge of linear algebra and basic differential calculus. The author describes, in detail, many interesting examples, including formulas which have not previously appeared in book form. Topics covered include the Haar measure and invariant integration, spherical harmonics, Fourier analysis and the heat equation, Poisson kernel, the Laplace equation and harmonic functions. Perfect for advanced undergraduates and graduates in geometric analysis, harmonic analysis and representation theory, the tools developed will also be useful for specialists in stochastic calculation and the statisticians. With numerous exercises and worked examples, the text is ideal for a graduate course on analysis on Lie groups.
Analysis on Lie Groups: An Introduction
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Editorial Reviews
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"The main themes are carefully explained and illustrated by well-chosen examples. He succeeds in putting a remarkable wealth of material into a 300-page book which will certainly serve as a basis for many courses on the subject."
Joachim Hilgert, Mathematical Reviews
Joachim Hilgert, Mathematical Reviews
Book Description
A self-contained and elementary presentation of Lie group theory, concentrating on analysis on Lie groups. The author describes in detail many interesting examples with topics ranging from Haar measure to harmonic functions. With numerous exercises and worked examples, it's ideal for a graduate course on analysis on Lie groups.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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recursion assumption, upper triangular group, invariant under the adjoint representation, highest weight vector, invariant differential form, group morphism, exponential map, derived representation, positive diagonal entries, algebra morphism Key Phrases - Capitalized Phrases (CAPs): (learn more)
Schur's Lemma, Proof Let, Peter-Weyl Theorem, Stone-Weierstrass Theorem, Generalised Taylor, Funk-Hecke Theorem Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
recursion assumption, upper triangular group, invariant under the adjoint representation, highest weight vector, invariant differential form, group morphism, exponential map, derived representation, positive diagonal entries, algebra morphism Key Phrases - Capitalized Phrases (CAPs): (learn more)
Schur's Lemma, Proof Let, Peter-Weyl Theorem, Stone-Weierstrass Theorem, Generalised Taylor, Funk-Hecke Theorem Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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