This is an announcement for the paper "Fourier transform of function on locally compact Abelian groups taking values in Banach spaces" by Yauhen Radyna and Anna Sidorik.
Abstract: 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.
Archive classification: math.FA
Mathematics Subject Classification: 46C15, 43A25
Remarks: 9 pages
The source file(s), Radyna_YM_Sidorik_AG_eng.tex: 30387 bytes, is(are) stored in gzipped form as 0808.4009.gz with size 10kb. The corresponding postcript file has gzipped size 89kb.
Submitted from: yauhen.radyna@gmail.com
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