The Michigan Mathematical Journal

Absolutely Convergent Fourier Series of Functions over Homogeneous Spaces of Compact Groups

Arash Ghaani Farashahi

Advance publication

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Abstract

This paper presents a systematic study for classical aspects of functions with absolutely convergent Fourier series over homogeneous spaces of compact groups. Let G be a compact group, H be a closed subgroup of G, and μ be the normalized G-invariant measure over the left coset space G/H associated with Weil’s formula with respect to the probability measures of G and H. We introduce the abstract notion of functions with absolutely convergent Fourier series in the Banach function space L1(G/H,μ). We then present some analytic characterizations for the linear space consisting of functions with absolutely convergent Fourier series over the compact homogeneous space G/H.

Article information

Source
Michigan Math. J., Advance publication (2019), 22 pages.

Dates
Received: 20 February 2018
Revised: 24 April 2018
First available in Project Euclid: 21 November 2019

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1574326881

Digital Object Identifier
doi:10.1307/mmj/1574326881

Subjects
Primary: 20G05: Representation theory 43A85: Analysis on homogeneous spaces
Secondary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 43A90: Spherical functions [See also 22E45, 22E46, 33C55]

Citation

Ghaani Farashahi, Arash. Absolutely Convergent Fourier Series of Functions over Homogeneous Spaces of Compact Groups. Michigan Math. J., advance publication, 21 November 2019. doi:10.1307/mmj/1574326881. https://projecteuclid.org/euclid.mmj/1574326881


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