# The Logvinenko-Sereda Theorem for the Fourier-Bessel transform

Abstract : The aim of this paper is to establish an analogue of Logvinenko-Sereda's theorem for the Fourier-Bessel transform (or Hankel transform) $\ff_\alpha$ of order $\alpha>-1/2$. Roughly speaking, if we denote by $PW_\alpha(b)$ the Paley-Wiener space of $L^2$-functions with Fourier-Bessel transform supported in $[0,b]$, then we show that the restriction map $f\to f|_\Omega$ is essentially invertible on $PW_\alpha(b)$ if and only if $\Omega$ 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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Journal articles

Cited literature [14 references]

https://hal.archives-ouvertes.fr/hal-00696009
Contributor : Saifallah Ghobber <>
Submitted on : Thursday, May 10, 2012 - 3:05:55 PM
Last modification on : Wednesday, October 28, 2020 - 2:20:03 PM
Long-term archiving on: : Saturday, August 11, 2012 - 2:35:19 AM

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### Identifiers

• HAL Id : hal-00696009, version 1
• ARXIV : 1205.2268

### Citation

Saifallah Ghobber, Philippe Jaming. The Logvinenko-Sereda Theorem for the Fourier-Bessel transform. Integral Transforms and Special Functions, Taylor & Francis, 2013, 24, pp.470-484. ⟨hal-00696009⟩

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