Harmonic Analysis on Symmetric Spaces and Applications II

of Volume II.- IV The Space Pnof PositivenxnMatrices.- 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.