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Volume 32, Issue 4
Classical Fourier Analysis over Homogeneous Spaces of Compact Groups

A. Ghaani Farashahi

Anal. Theory Appl., 32 (2016), pp. 339-354.

Published online: 2016-10

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  • 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 $L^2(G/H,\mu)$.

  • AMS Subject Headings

20G05, 43A85, 43A32, 43A40, 43A90

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-32-339, author = {A. Ghaani Farashahi}, title = {Classical Fourier Analysis over Homogeneous Spaces of Compact Groups}, journal = {Analysis in Theory and Applications}, year = {2016}, volume = {32}, number = {4}, pages = {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 $L^2(G/H,\mu)$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2016.v32.n4.3}, url = {http://global-sci.org/intro/article_detail/ata/4675.html} }
TY - JOUR T1 - Classical Fourier Analysis over Homogeneous Spaces of Compact Groups AU - A. Ghaani Farashahi JO - Analysis in Theory and Applications VL - 4 SP - 339 EP - 354 PY - 2016 DA - 2016/10 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n4.3 UR - https://global-sci.org/intro/article_detail/ata/4675.html KW - Compact group, homogeneous space, dual space, Fourier transform, Plancherel (trace) formula, Peter-Weyl Theorem. AB -

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 $L^2(G/H,\mu)$.

A. Ghaani Farashahi. (2016). Classical Fourier Analysis over Homogeneous Spaces of Compact Groups. Analysis in Theory and Applications. 32 (4). 339-354. doi:10.4208/ata.2016.v32.n4.3
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