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.
Rezensionen / Stimmen
"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
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Illustrationen
Worked examples or Exercises; 6 Line drawings, unspecified
Maße
Höhe: 235 mm
Breite: 157 mm
Dicke: 23 mm
Gewicht
ISBN-13
978-0-521-71930-8 (9780521719308)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Jacques Faraut is Professeur Emerite in the Institut de Mathematiques de Jussieu at the Universite Pierre et Marie Curie in Paris.
Autor*in
Universite de Paris VI (Pierre et Marie Curie)
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.
