Harmonic Analysis on Symmetric Spaces and Applications II - Brossura

Terras, Audrey

9780387966632: Harmonic Analysis on Symmetric Spaces and Applications II

Brossura

ISBN 10: 0387966633 ISBN 13: 9780387966632

Casa editrice: Springer Verlag, 1988

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Well, finally, here it is-the long-promised "Revenge of the Higher Rank Symmetric Spaces and Their Fundamental Domains." When I began work on it in 1977, I would probably have stopped immediately if someone had told me that ten years would pass before I would declare it "finished." Yes, I am declaring it finished-though certainly not perfected. There is a large amount of work going on at the moment as the piles of preprints reach the ceiling. Nevertheless, it is summer and the ocean calls. So I am not going to spend another ten years revising and polishing. But, gentle reader, do send me your corrections and even your preprints. Thanks to your work, there is an Appendix at the end of this volume with corrections to Volume I. I said it all in the Preface to Volume I. So I will try not to repeat myself here. Yes, the "recent trends" mentioned in that Preface are still just as recent.

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Contenuti

of Volume II.- IV The Space Pnof Positiven�nMatrices.- 4.1. Geometry and Analysis on Pn.- 4.1.0. Introduction.- 4.1.1. Elementary Results.- 4.1.2. Geodesics and Arc Length.- 4.1.3. Measure and Integration on Pn.- 4.1.4. Differential Operators on Pn.- 4.1.5. A List of the Main Formulas Derived in Section 1.- 4.1.6. An Application to Multivariate Statistics.- 4.2. Special Functions on Pn.- 4.2.1. Power and Gamma Functions.- 4.2.2.K-Bessel Functions.- 4.2.3. Spherical Functions.- 4.2.4. The Wishart Distribution.- 4.3. Harmonic Analysis on Pnin Polar Coordinates.- 4.3.1. Properties of the Helgason-Fourier Transform on Pn.- 43.2. Beginning of the Discussion of Part (1) of Theorem 1―Steps 1 and 2.- 4.3.3. End of the Discussion of Part (1) of Theorem 1―Steps 3 and 4.- 4.3.4. Applications.- 4.3.5. Other Directions in the Labyrinth.- 4.4. Fundamental Domains for Pn/GL(n?).- 4.4.1. Introduction.- 4.4.2. Minkowski’s Fundamental Domain.- 4.4.3. Grenier’s Fundamental Domain.- 4.4.4. Integration over Fundamental Domains.- 4.5. Automorphic Forms forGL(n?) and Harmonic Analysis on Pn/GL(n?).- 4.5.1. Analytic Continuation of Eisenstein Series by the Method of Inserting.- Larger Parabolic Subgroups.- 4.5.2. Hecke Operators and Analytic Continuation ofL-Functions Associated to Modular Forms by the Method of Theta Functions.- 4.5.3. Fourier Expansions of Eisenstein Series.- 4.5.4. Remarks on Harmonic Analysis on the Fundamental Domain.- V The General Noncompact Symmetric Space.- 5.1. Geometry and Analysis onG/K.- 5.2. Geometry and Analysis on ?\G/K.- Appendix Corrections to Volume I.- Bibliography for Volume II.