Abstract
The aim of this paper is to establish an analogue of Logvinenko-Sereda's theorem for the Fourier-Bessel transform (or Hankel transform) ℱ
α
of order α>−½. Roughly speaking, if we denote by PW
α
(b) the Paley-Wiener space of L
2
-functions with the Fourier-Bessel transform supported in [0, b], then we show that the restriction map f→f|
Ω
is essentially invertible on PW
α
(b) if and only if Ω 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.