Ghaani Farashahi, A orcid.org/0000-0003-1580-512X (2017) Abstract operator-valued Fourier transforms over homogeneous spaces of compact groups. Groups, Geometry, and Dynamics, 11 (4). pp. 1437-1467. ISSN 1661-7207
Abstract
This paper presents a systematic theoretical study for the abstract notion of operator-valued Fourier transforms over homogeneous spaces of compact groups. Let GG be a compact group, HH be a closed subgroup of GG, and μμ be the normalized GG-invariant measure over the left coset space G/HG/H associated to the Weil's formula. We introduce the generalized notions of abstract dual homogeneous space G/HˆG/H^ for the compact homogeneous space G/HG/H and also the operator-valued Fourier transform over the Banach function space L1(G/H,μ)L1(G/H,μ). We prove that the abstract Fourier transform over G/HG/H satisfies the Plancherel formula and the Poisson summation formula.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | 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 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 23 Mar 2020 12:39 |
Last Modified: | 23 Mar 2020 12:39 |
Status: | Published |
Publisher: | European Mathematical Society |
Identification Number: | 10.4171/ggd/434 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:158641 |