| Type de publication : |
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Preprint, Working Paper, Document sans référence, etc. |
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| Domaine : |
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Mathématiques/Analyse classique
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| Titre : |
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THE LOGVINENKO-SEREDA THEOREM FOR THE FOURIER-BESSEL TRANSFORM |
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| Auteur(s) : |
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Saifallah Ghobber ( ) 1, 2, Philippe Jaming 3 |
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| Laboratoire : |
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| Résumé : |
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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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Langue du texte
intégral : |
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Anglais |
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| Mots Clés : |
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Fourier-Bessel transform – Hankel transform – uncertainty principle – strong annihilating pairs |
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| Classification : |
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42A68; 42C20 |
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