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 anyhomogeneous space of compact groups separates points of the homogeneous space in some sense.
Citation
Arash Ghaani Farashahi. "Trigonometric polynomials over homogeneous spaces of compact groups." Adv. Oper. Theory 2 (1) 87 - 97, Winter 2017. https://doi.org/10.22034/aot.1701-1090
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