Jacques Faraut

Analysis on Lie Groups (eBook, PDF)

An Introduction

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 22. Mai 2008
• Englisch
• ISBN-13: 9780511421105
• Artikelnr.: 38184393

Autorenporträt

Jacques Faraut is Professeur Émérite in the Institut de Mathématiques de Jussieu at the Université Pierre et Marie Curie in Paris.

Inhaltsangabe

Preface
1. The linear group
2. The exponential map
3. Linear Lie groups
4. Lie algebras
5. Haar measure
6. Representations of compact groups
7. The groups SU(2) and SO(3), Haar measure
8. Analysis on the group SU(2)
9. Analysis on the sphere
10. Analysis on the spaces of symmetric and Hermitian matrices
11. Irreducible representations of the unitary group
12. Analysis on the unitary group
Bibliography
Index.