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

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 L2(G/H,\mu).
• Keywords

Compact group homogeneous space dual space Fourier transform Plancherel (trace) formula Peter-Weyl Theorem

20G05 43A85 43A32 43A40 43A90

@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 L2(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 KW - homogeneous space KW - dual space KW - Fourier transform KW - Plancherel (trace) formula KW - 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 L2(G/H,\mu).