Advances in Operator Theory

Trigonometric polynomials over homogeneous spaces of compact groups

Arash Ghaani Farashahi

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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.

Article information

Adv. Oper. Theory, Volume 2, Number 1 (2017), 87-97.

Received: 9 January 2017
Accepted: 28 January 2017
First available in Project Euclid: 4 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 43A85: Analysis on homogeneous spaces
Secondary: 20G05: Representation theory 47A67: Representation theory

compact homogeneous space $G$-invariant measure compact group dual space unitary representation irreducible representation trigonometric polynomials


Ghaani Farashahi, Arash. Trigonometric polynomials over homogeneous spaces of compact groups. Adv. Oper. Theory 2 (2017), no. 1, 87--97. doi:10.22034/aot.1701-1090.

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