Format:
Online-Ressource
ISBN:
9783642111174
Series Statement:
C.I.M.E. Summer Schools 82
Content:
This title includes: Lectures - A. Auslander, R. Tolimeri - Nilpotent groups and abelian varieties, M Cowling - Unitary and uniformly bounded representations of some simple Lie groups, M. Duflo - Construction de representations unitaires d'un groupe de Lie, R. Howe - On a notion of rank for unitary representations of the classical groups, V.S. Varadarajan - Eigenfunction expansions of semisimple Lie groups, and R. Zimmer - Ergodic theory, group representations and rigidity; and, Seminars - A. Koranyi - Some applications of Gelfand pairs in classical analysis
Note:
Description based upon print version of record
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Harmonic Analysis and Group Representation; Copyright Page; Contents; Lectures on Nilpotent Groups and Abelian Varieties; Introduction; I. Associative Algebras and Nilpotent Algebraic Croups; 2. The Jacobi Variety of a Riemann Surface 2. The Jacobi Variety of a Riemann Surface and Abelian Varieties; 3. Morphisms of Abelian Varieties and the Structure of Riemann Matrices; 4. Riemann Matrices Whose Multiplier Algebras are Totally Real Fields; 5. The Involution Problem for Division Algebras of the First Kind (Part I); 6. The Involution Problem for Division Algebras of the First Kid (Conclusion
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7. Existence of Riemann Matrices for Division Algebras of the First KindReferences; Unitary and Uniformly Bounded Representations of Some Lie Groups; 0. Introduction; 1. Analysis on Heisenberg Grows. I; 2. Analysis on Heisenberg Groups. II; 3. Representations of Heisenberg Grooups.; 4. Some Simple Groups; 5. The Principal Series and the Intertwining Operators; 6. Lp-Harmonic Analysis on Some Simple Groups; 7. Uniformly Bounded Representations and Complementary Series; 8. An Extrapolation Priciple; References; Construction De Representation Unitaires D'un Group De Lie; Resume; Summery
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IntroductionAppendice : Parametrization of the Set of Regular Orbits of the Coadjoint Representation of a Lie Group; Commentaires; References; On a Notation of Rank for Unitary Representations of the Classical Groups; 1. Review of the Heisenberg group and the oscillator representation; 2. The Nm -rank of representations of Sp; 3: No -rank and regularity; 4. Description of (Image); 5. Exemples; 6: Asymptotics of matrix coefficients, generalities; 7: Asymptotics of matrix coefficients for semisimple groups; 8: Asymptotics of matrix coefficients and rank for Sp.; References
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Some Applications of Gelfand Pairs in Classical AnalysisIntroduction; 1. Vector-valued functions on spheres; 2. Biradial functions on nilpotent groups; References; Eigenfunction Expansions on Semisimple Lie Groups; 1. Representations of the Principal Series. Harish Chandra's Plancherel formula; 2. Eigenfunction expansions on G. The case of spherical functions.; 3. Asymptotic behaviour of spherical eigenfunctions; 4. Wave packets in spherical Schwartz space; 5. Asymptotic behaviour of tempered eigenfunctions for 8. The constant term; 6. Wave packets in Schwaxtz space
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7. The Eisenstein integral and the c-functions8. The Plancherel measure and the Plancherel formula; Acknowledgement; References; Ergodic Theory, Group Representations, and Rigidity; I. Basic Notions; 2. Ergodicity Theorems; 3. Cocycles; 4. Generalized Discrete Spectrum; 5. Amenability; 6. Rigidity: The Mostow-Margulis Theorem and a Generalization to Ergodic Actions; 7. Complements to the Rigidity Theorem for Ergodic Actions: Foliations by Symmetric Spaces, and Kazhdan's Property (T); 8. Margulis' Finiteness Theorem; 9. Margulis' Arithmeticity Theorem; References;
Language:
English
Keywords:
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