Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group pp 269-334 | Cite as

# The Case of Symmetric Spaces *X*=*G*/*K* of Noncompact Type

## Abstract

Methods are developed for studying mean periodic functions on symmetric spaces *X*=*G*/*K* of noncompact type. The constructions are based on three main ingredients. The first is the Fourier decomposition on *X*, the second is the Eisenstein–Harish-Chandra integrals and their generalizations, and the third is the Helgason Fourier transform. This material is presented at the beginning of the chapter. The theory of transmutation operators associated with the inversion formula for the *δ*-spherical transform is then developed. In the case rank *X*=1, the theory is constructed in a more explicit and concrete form. At the end of the chapter various applications to questions connected with eigenfunctions expansions of Laplacian are considered.

## Keywords

Entire Function Symmetric Space Spherical Function Matrix Entry Beltrami Operator## Preview

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