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 F α ( f ) cannot both have support of finite measure. The second result states that the supports of f and F α ( 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 C 0 -function are linearly independent. We also extend Farisʹs local uncertainty principle to the Fourier–Bessel transform.