JournalsggdVol. 13, No. 2pp. 511–547

Fourier–Stieltjes transforms over homogeneous spaces of compact groups

  • Arash Ghaani Farashahi

    University of Leeds, UK
Fourier–Stieltjes transforms over homogeneous spaces of compact groups cover

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Abstract

This paper presents a unified operator theory approach to the abstract notion of Fourier–Stieltjes transforms for Banach measure algebras over homogeneous spaces of compact groups. Let HH be a closed subgroup of the compact group GG and G/HG/H be the left coset space associated to the subgroup HH in GG. Also, let M(G/H)M(G/H) be the Banach measure space consists of all (bounded) complex Radon measures over the compact homogeneous space G/HG/H. We then study theoretical aspects of operator-valued Fourier–Stieltjes transform for the Banach measure algebras M(G/H)M(G/H). We shall also present a uniqueness theorem for the abstract Fourier–Stieltjes transforms.

Cite this article

Arash Ghaani Farashahi, Fourier–Stieltjes transforms over homogeneous spaces of compact groups. Groups Geom. Dyn. 13 (2019), no. 2, pp. 511–547

DOI 10.4171/GGD/496