Advances in Operator Theory

Trigonometric polynomials over homogeneous spaces of compact groups

Arash Ghaani Farashahi

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

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512431516

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

Zentralblatt MATH identifier
1370.43005

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

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

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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