Peter-Weyl Theorem for Homogeneous Spaces of Compact Groups

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Arash Ghaani Farashahi, Peter-Weyl Theorem for Homogeneous Spaces of Compact Groups, Int. J. Anal. Appl., 13 (1) (2017), 22-31.

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Arash Ghaani Farashahi

Abstract

This paper presents a structured formalism for a constructive generalization of the Peter-Weyl Theorem over homogeneous spaces of compact groups. Let H be a closed subgroup of a compact group G and µ be the normalized G-invariant measure on the compact left coset space G/H. We then present an abstract T H -version of the Peter-Weyl Theorem for the Hilbert function space L2 (G/H, µ).

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