3028 articles  [version française]
 HAL: hal-00696009, version 1
 arXiv: 1205.2268
 THE LOGVINENKO-SEREDA THEOREM FOR THE FOURIER-BESSEL TRANSFORM
 Saifallah Ghobber 1, 2, Philippe Jaming 3
 (2012-05-10)
 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.
 1: Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) Université d'Orléans – CNRS : UMR7349 2: Analyse harmonique et fonctions spéciales Faculté des Sciences de Tunis 3: Institut de Mathématiques de Bordeaux (IMB) CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
 Subject : Mathematics/Classical Analysis and ODEs
 Keyword(s): Fourier-Bessel transform – Hankel transform – uncertainty principle – strong annihilating pairs
Attached file list to this document:
 PDF
 L-S120424.pdf(208.9 KB)
 PS
 L-S120424.ps(713.9 KB)
 hal-00696009, version 1 http://hal.archives-ouvertes.fr/hal-00696009 oai:hal.archives-ouvertes.fr:hal-00696009 From: Saifallah Ghobber <> Submitted on: Thursday, 10 May 2012 15:05:55 Updated on: Thursday, 10 May 2012 16:02:21