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March 2020 Absolutely Convergent Fourier Series of Functions over Homogeneous Spaces of Compact Groups
Arash Ghaani Farashahi
Michigan Math. J. 69(1): 179-200 (March 2020). DOI: 10.1307/mmj/1574326881

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.

Citation

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Arash Ghaani Farashahi. "Absolutely Convergent Fourier Series of Functions over Homogeneous Spaces of Compact Groups." Michigan Math. J. 69 (1) 179 - 200, March 2020. https://doi.org/10.1307/mmj/1574326881

Information

Received: 20 February 2018; Revised: 24 April 2018; Published: March 2020
First available in Project Euclid: 21 November 2019

zbMATH: 07208929
MathSciNet: MR4071349
Digital Object Identifier: 10.1307/mmj/1574326881

Subjects:
Primary: 20G05, 43A85
Secondary: 43A30, 43A90

Rights: Copyright © 2020 The University of Michigan

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Vol.69 • No. 1 • March 2020
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