  The aim of this paper is to establish an analogue of Logvinenko-Sereda's
theorem for the Fourier-Bessel transform (or Hankel transform) $\ff_\alpha$ of
order $\alpha>-1/2$. Roughly speaking, if we denote by $PW_\alpha(b)$ the
Paley-Wiener space of $L^2$-functions with Fourier-Bessel transform supported
in $[0,b]$, then we show that the restriction map $f\to f|_\Omega$ is
essentially invertible on $PW_\alpha(b)$ if and only if $\Omega$ is
sufficiently dense. Moreover, we give an estimate of the norm of the inverse
map. As a side result we prove a Bernstein type inequality for the
Fourier-Bessel transform.
