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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Journal of Mathematical Analysis and Applications, Elsevier, 2011, 377, pp.501-515. 〈10.1080/10652469.2012.708868〉
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Contributeur : Philippe Jaming <>
Soumis le : jeudi 9 septembre 2010 - 10:31:02
Dernière modification le : mardi 18 décembre 2018 - 10:56:29
Document(s) archivé(s) le : vendredi 10 décembre 2010 - 02:42:55

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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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