الفهرس 
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Abstract
In this thesis, our purpose is the study of expansions of eigenfunctions into series which is very often called harmonic analysis. In particular, we study harmonic analysis of generalized kernels, in Hilbert spaces. Namely, we obtain the necessary and sufficient conditions for a matrix kernel to be positive definite and G-Invariant. In order to explain the idea behind the construction, we restatethe basic construction of the integral representation of positive-definite invariant kernels.