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Strong annihilating pairs for the Fourier-Bessel transform. (English) Zbl 1210.42016

Summary: 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 \(\mathcal F_\alpha (f)\) cannot both have support of finite measure. The second result states that the supports of \(f\) and \(\mathcal F_\alpha (f)\) cannot both be \((\epsilon ,\alpha )\)-thin, this extending a result of Shubin, Vakilian and Wolff. As a side result we prove that the dilation of a \(\mathcal C_0\)-function are linearly independent. We also extend Faris’s local uncertainty principle to the Fourier-Bessel transform.

MSC:

42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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