Year: 2016
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 4 : pp. 339–354
Abstract
This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let $G$ be a compact group and $H$ be a closed subgroup of $G$. Let $G/H$ be the left coset space of $H$ in $G$ and $\mu$ be the normalized $G$-invariant measure on $G/H$ associated to the Weil's formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space $L^2(G/H,\mu)$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2016.v32.n4.3
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 4 : pp. 339–354
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Compact group homogeneous space dual space Fourier transform Plancherel (trace) formula Peter-Weyl Theorem.