Format:
Online-Ressource
ISBN:
9783642110122
Series Statement:
C.I.M.E. Summer Schools 53
Content:
A. Figa Talamanca: Random Fourier series on compact groups.- S. Helgason: Representations of semisimple Lie groups.- H. Jacquet: Representations des groupes lineaires p-adiques.- G.W. Mackey: Infinite-dimensional group representations and their applications
Note:
Description based upon print version of record
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Theory of Group Representations and Fourier Analysis; Copyright Page; Contents; Introduction; Chapter I; Chapter II; References; Representations of Semisimple lie Groups; 1. Complex semisimple lie algebras; 2. Finite dimensional representations; 3. Real semisimple lie groups; 4. Infinite-dimensional representations; 5. Fourier analysis of spherical functions; References; Representations des Groupes Lineaires p-Adiques; 1. Introduction; 2. Notions générales; 3. Sous- groupes paraboliques; 4. Représentations absolument Pointus; 5. Représentations induites
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6. Etude élémentaire des représentations induites7. Représentations spéciales; 8. Fonction sphériques; 9. Caracteres et représentations induites; 10. Bibliogrphie; Infinite Dimensional Group Representations and Their Applications; 1. Introduction; 2. Some basic facts and definitions; 3. Invariant measures and Fourier analysis; 4. Ston's theorem and the connection with spectral theory; 5. The spectral theorem and its generalizations; 6. Measure classes and multiplicity free representations; 7. Reduction to the multiplicity free case; 8. The extension to the non commutative case
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9. Non type I groups and the connection with the theory of von Neumann algebras10. The inducing construction; 11. Some properties of the inducing construction; 12. The imprimitivity theorem; 13. Irreducible induced representations; 14. Intertwining operators for induced representations; 15. Plancherel measures for induced representations; 16. Projective unitary representations; 17. Ergodicity and virtual subgroups; 18. Connections with the theory of probability; 19. Applications to the theory of automorphic forms; 20. Applications to number theory; 21. Applications to quantum mechanics
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References
Language:
English
Keywords:
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