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

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

2008-03-25

arxiv.org/abs/0803.3646v1

Yauhen Radyna, Yakov Radyno, Anna Sidorik, Characterizing Hilbert spaces using Fourier transform over the field of p-adic numb

Mathematics

Functional Analysis

6 pages, translation to English

Scientific paper

We 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.

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