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arXiv · 1205.2268

The Logvinenko-Sereda Theorem for the Fourier-Bessel transform

Saifallah Ghobber·Philippe Jaming
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Abstract

The aim of this paper is to establish an analogue of Logvinenko-Sereda's theorem for the Fourier-Bessel transform (or Hankel transform) $\ff_α$ of order $α>-1/2$. Roughly speaking, if we denote by $PW_α(b)$ the Paley-Wiener space of $L^2$-functions with Fourier-Bessel transform supported in $[0,b]$, then we show that the restriction map $f\to f|_Ω$ is essentially invertible on $PW_α(b)$ if and only if $Ω$ is sufficiently dense. Moreover, we give an estimate of the norm of the inverse map. As a side result we prove a Bernstein type inequality for the Fourier-Bessel transform.

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Saifallah Ghobber, Philippe Jaming. 2012-05-10. The Logvinenko-Sereda Theorem for the Fourier-Bessel transform. https://doi.org/10.1080/10652469.2012.708868

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