Spectral Analysis on Standard Locally Homogeneous Spaces

1 Introduction.- 2 Method of proof.- Part I Generalities.- 3 Reminders: spectral analysis on spherical homogeneous spaces.- 4 Discrete spectrum of type I and II.- 5 Di?erential operators coming from ?? and from the fiber ??.- Part II Proof of the theorems of Chapter 1.- 6 Essential self-adjointness of the Laplacian.- 7 Transfer of Riemannian eigenfunctions and spectral decomposition.- 8 Consequences of conditions (A) and (B) on representations of G and ??.- 9 The maps i??,?? and p??,?? preserve type I and type II.- 10 Infinite discrete spectrum of type II.- Part III Representation-theoretic description of the discrete spectrum.- 11 A conjectural picture.- 12 The discrete spectrum in terms of group representations.

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• Grupos e teoria do grupo
• Análise complexa, variáveis ??complexas

Laplacian;invariant differential operator;pseudo-Riemannian manifold;reductive symmetric space;proper action;spherical variety;real spherical homogeneous space;branching law