Fourier analysis on domains in compact groups
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AbstractLet Omega be a measurable subset of a compact group G of positive Haar measure. Let mu: pi bar right arrow mu(pi) be a non-negative function defined on the dual space (G) over cap and let L-2(mu) be the corresponding Hilbert space which consists of elements (xi(pi))(pi is an element of suppp mu) satisfying Sigma mu(pi) Tr(xi(pi)xi(pi)*) < infinity, where xi(pi) is a linear operator on the representation space of pi, and is equipped with the inner product: (xi(pi))), (eta(pi))) = Sigma mu(pi) Tr(xi(pi) eta(pi)*). We show that the Fourier transform gives an isometric isomorphism from L-2(Omega) onto L-2 (mu) if and only if the restrictions to Omega of all matrix coordinate functions root mu(pi) pi(ij), pi is an element of supp mu, constitute an orthonormal basis for L-2(Omega). Finally compact connected Lie groups case is studied. (C) 2006 Elsevier Inc. All rights reserved.
All Author(s) ListLeung CW
Journal nameJournal of Functional Analysis
Detailed descriptionAvailable online.
Volume Number238
Issue Number2
Pages636 - 648
LanguagesEnglish-United Kingdom
KeywordsC-infinity vectors; compact groups; Fourier transform; spectral pairs
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2021-08-04 at 00:48