Geodesic
Abstract operator-valued Fourier transforms over homogeneous spaces of compact groups
Arash Ghaani Farashahi1
1University of Vienna, Austria
Groups, geometry, and dynamics, Tome 11 (2017) no. 4, pp. 1437-1467

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DOI

This paper presents a systematic theoretical study for the abstract notion of operator-valued Fourier transforms 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 to the Weil's formula. We introduce the generalized notions of abstract dual homogeneous space G/H​ for the compact homogeneous space G/H and also the operator-valued Fourier transform over the Banach function space L1(G/H,μ). We prove that the abstract Fourier transform over G/H satisfies the Plancherel formula and the Poisson summation formula.
DOI : 10.4171/ggd/434
Classification : 20-XX, 43-XX
Mots-clés : Compact group, homogeneous space, coset space,Weil’s formula, dual homogeneous space, trigonometric polynomial, Fourier transform, Plancherel (trace) formula, Hausdorff–Young inequality, inversion formula, Poisson summation formula

Arash Ghaani Farashahi  1

1 University of Vienna, Austria 
Arash Ghaani Farashahi. Abstract operator-valued Fourier transforms over homogeneous spaces of compact groups. Groups, geometry, and dynamics, Tome 11 (2017) no. 4, pp. 1437-1467. doi: 10.4171/ggd/434
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     title = {Abstract operator-valued {Fourier} transforms over homogeneous spaces of compact groups},
     journal = {Groups, geometry, and dynamics},
     pages = {1437--1467},
     year = {2017},
     volume = {11},
     number = {4},
     doi = {10.4171/ggd/434},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/434/}
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