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arXiv · 1009.1710

Strong annihilating pairs for the Fourier-Bessel transform

Saifallah Ghobber·Philippe Jaming
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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 $\mathcal{F}_α(f)$ cannot both have support of finite measure. The second result states that the supports of $f$ and $\mathcal{F}_α(f)$ cannot both be $(\eps,α)$-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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Saifallah Ghobber, Philippe Jaming. 2010-09-09. Strong annihilating pairs for the Fourier-Bessel transform. https://doi.org/10.1016/j.jmaa.2010.11.015

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