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arXiv:0808.4009 [math.FA]AbstractReferencesReviewsResources

Fourier transform of function on locally compact Abelian groups taking value in Banach spaces

Yauhen Radyna, Anna Sidorik

Published 2008-08-29Version 1

We consider Fourier transform of vector-valued functions on a locally compact group $G$, which take value in a Banach space $X$, and are square-integrable in Bochner sense. If $G$ is a finite group then Fourier transform is a bounded operator. If $G$ is an infinite group then Fourier transform $F: L_2(G,X)\to L_2(\widehat G,X)$ is a bounded operator if and only if Banach space $X$ is isomorphic to a Hilbert one.

Comments: 9 pages
Categories: math.FA
Subjects: 46C15, 43A25
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