Bibliothèque de L'IMIST/CNRST

Mean periodic functions on homogeneous spaces is a very active research area, having close connections to harmonic analysis, complex analysis, integral geometry, and analysis on symmetric spaces. This book presents systematic and unified treatment of the theory of mean periodic functions on homogeneous spaces.

Includes bibliographical references (p. [647]-660) and index.

General consideration -- Analogues of the Beltrami-Klein model for rank one symmetric spaces of noncompact type -- Realizations of rank one symmetric spaces of compact type -- Realizations of the Irreducible components of the quasi-regular representation of groups transitive on spheres. Invariant subspaces; Non-Euclidean analogues of plane waves -- Preliminaries -- Some special functions -- Exponential expansions -- Multidimensional Euclidean case -- The case of symmetric spaces X=G/K of noncompact type -- The case of compact symmetric spaces -- The case of phase space --

Mean periodic functions on subsets of the real line -- Mean periodic functions on multidimensional domains -- Mean periodic functions on G/K -- Mean periodic functions on compact symmetric spaces of rank one -- Mean periodicity on phase space and the Heisenberg group -- A new look at the Schwartz theory -- Recent developments in the spectral analysis problem for higher dimensions -- E'..(X) spectral analysis on domains of noncompact symmetric spaces of arbitrary rank -- Spherical spectral analysis on subsets of compact symmetric spaces of rank one.