# Strong annihilating pairs for the Fourier-Bessel transform

Abstract : 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-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 $(\eps,\alpha)$-thin, this extending a result of Shubin-Vakilian-Wolff. As a side result we prove that the dilation of a $\cc_0$-function are linearly independent. We also extend Faris's local uncertainty principle to the Fourier-Bessel transform.
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https://hal.archives-ouvertes.fr/hal-00516289
Contributor : Philippe Jaming <>
Submitted on : Thursday, September 9, 2010 - 10:31:02 AM
Last modification on : Tuesday, December 18, 2018 - 10:56:29 AM
Document(s) archivé(s) le : Friday, December 10, 2010 - 2:42:55 AM

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### Citation

Saifallah Ghobber, Philippe Jaming. Strong annihilating pairs for the Fourier-Bessel transform. Journal of Mathematical Analysis and Applications, Elsevier, 2011, 377, pp.501-515. ⟨10.1080/10652469.2012.708868⟩. ⟨hal-00516289⟩

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