Characterizing Hilbert spaces using Fourier transform over the field of p-adic numbers

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dc.creatorRadyna, Yauhen
dc.creatorRadyno, Yakov
dc.creatorSidorik, Anna
dc.date2008-03-25
dc.date.accessioned2026-07-07T09:58:58Z
dc.date.available2026-07-07T09:58:58Z
dc.descriptionWe characterize Hilbert spaces in the class of all Banach spaces using Fourier transform of vector-valued functions over the field $Q_p$ of $p$-adic numbers. Precisely, Banach space $X$ is isomorphic to a Hilbert one if and only if Fourier transform $F: L_2(Q_p,X)\to L_2(Q_p,X)$ in space of functions, which are square-integrable in Bochner sense and take value in $X$, is a bounded operator.
dc.description6 pages, translation to English
dc.identifierhttps://arxiv.org/abs/0803.3646
dc.identifierhttp://arxiv.org/abs/0803.3646
dc.identifierYauhen Radyna, Yakov Radyno, Anna Sidorik, Characterizing Hilbert spaces using Fourier transform over the field of p-adic numbers. Dokl. Nats. Akad. Nauk Belarusi, vol.51, No.5 (2007), p.17--22 (in russian)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167873
dc.subjectFunctional Analysis
dc.subject46C15, 43A25
dc.titleCharacterizing Hilbert spaces using Fourier transform over the field of p-adic numbers
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