### Trigonometric polynomials over homogeneous spaces of compact groups

Arash Ghaani Farashahi

#### 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.

#### Article information

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

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

https://projecteuclid.org/euclid.aot/1512431516

Digital Object Identifier
doi:10.22034/aot.1701-1090

Mathematical Reviews number (MathSciNet)
MR3730357

Zentralblatt MATH identifier
1370.43005

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

#### Citation

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. https://projecteuclid.org/euclid.aot/1512431516

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