2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167873We 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.6 pages, translation to EnglishFunctional Analysis46C15, 43A25text