Trigonometric polynomials over homogeneous spaces of compact groups

Document Type: Original Article

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Abstract

This paper presents a systematic study for trigonometric polynomials over homogeneous spaces of compact groups.
Let $H$ be a closed subgroup of a compact group $G$. Using the abstract notion of dual space $\widehat{G/H}$, we introduce the space of trigonometric polynomials $\mathrm{Trig}(G/H)$ over the compact homogeneous space $G/H$.
As an application for harmonic analysis of trigonometric polynomials, we prove that the abstract dual space of any
homogeneous space of compact groups separates points of the homogeneous space in some sense.

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