The Logvinenko-Sereda Theorem for the Fourier-Bessel transform
GHOBBER, Saifallah
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Analyse harmonique et fonctions spéciales
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Analyse harmonique et fonctions spéciales
GHOBBER, Saifallah
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Analyse harmonique et fonctions spéciales
< Reduce
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Analyse harmonique et fonctions spéciales
Language
en
Article de revue
This item was published in
Integral Transforms and Special Functions. 2013, vol. 24, p. 470-484
Taylor & Francis
English 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 $PW_\alpha(b)$ ...Read more >
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.Read less <
English Keywords
Fourier-Bessel transform
Hankel transform
uncertainty principle
strong annihilating pairs
Origin
Hal imported