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

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dc.creatorRadyna, Yauhen
dc.creatorSidorik, Anna
dc.date2008-08-29
dc.date.accessioned2026-07-07T09:59:24Z
dc.date.available2026-07-07T09:59:24Z
dc.descriptionWe 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.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/0808.4009
dc.identifierhttp://arxiv.org/abs/0808.4009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168008
dc.subjectFunctional Analysis
dc.subject46C15, 43A25
dc.titleFourier transform of function on locally compact Abelian groups taking value in Banach spaces
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