Analysis on Lie Groups: An Introduction

Jacques Faraut

doi:10.1017/CBO9780511755170

The subject of analysis on Lie groups comprises an eclectic group of topics which can be treated from many different perspectives. This self-contained text concentrates on the perspective of analysis, to the topics and methods of non-commutative harmonic analysis, assuming only elementary knowledge of linear algebra and basic differential calculus. The author avoids unessential technical discussions and instead describes in detail many interesting examples, including formulae 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.

"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

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Analysis on Lie Groups

An Introduction

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Preface
pp ix-x

1 - The linear group
pp 1-17

2 - The exponential map
pp 18-35

3 - Linear Lie groups
pp 36-49

4 - Lie algebras
pp 50-73

5 - Haar measure
pp 74-94

6 - Representations of compact groups
pp 95-126

7 - The groups SU(2) and SO(3), Haar measures and irreducible representations
pp 127-157

8 - Analysis on the group SU(2)
pp 158-185

9 - Analysis on the sphere and the Euclidean space
pp 186-230

10 - Analysis on the spaces of symmetric and Hermitian matrices
pp 231-248

11 - Irreducible representations of the unitary group
pp 249-273

12 - Analysis on the unitary group
pp 274-298

Bibliography
pp 299-300

Index
pp 301-302

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Analysis on Lie Groups

An Introduction

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