Strong annihilating pairs for the Fourier-Bessel transform

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:377

Article

Ghobber, Saifallah^2,3  Jaming, Philippe^1,2 

[1] Univ Bordeaux 1, Inst Math Bordeaux, UMR 5251, Cours Liberat, F-33405 Talence, France

[2] Univ Orleans, Fac Sci, MAPMO Federat Denis Poisson, F-45067 Orleans 2, France

[3] Univ Tunis El Manar, Fac Sci Tunis, Dept Math, Tunis 1060, Tunisia

关键词: Fourier-Bessel transform;    Hankel transform;    Uncertainty principle;    Annihilating pairs;   

DOI  :  10.1016/j.jmaa.2010.11.015

来源: Elsevier

【 摘 要 】

The aim of this paper is to prove two new uncertainty principles for the Fourier-Bessel transform (or Hankel transform). The first of these results is an extension of a result of Amrein, Berthier and Benedicks, it states that a non-zero function f and its Fourier-Bessel transform F-alpha(f) cannot both have support of finite measure. The second result states that the supports of f and F-alpha(f) cannot both be (epsilon, alpha)-thin, this extending a result of Shubin, Vakilian and Wolff. As a side result we prove that the dilation of a C-0-function are linearly independent. We also extend Faris's local uncertainty principle to the Fourier-Bessel transform. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free