  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.
