Strong annihilating pairs for the Fourier-Bessel transform

The aim of this paper is to prove two new uncertainty principles for the Fourier-Bessel transform (or Hankel transform). The first of these results is an extension of a result of Amrein, Berthier and Benedicks, it states that a non-zero function f and its Fourier-Bessel transform Fα(f) cannot both have support of finite measure. The second result states that the supports of f and Fα(f) cannot both be (ε,α)-thin, this extending a result of Shubin, Vakilian and Wolff. As a side result we prove that the dilation of a C0-function are linearly independent. We also extend Faris's local uncertainty principle to the Fourier-Bessel transform.