Phase space localization of orthonormal sequences in Lα2(R+)

JOURNAL OF APPROXIMATION THEORY

卷:189

Article

Ghobber, Saifallah

关键词: Hankel transform;    Uncertainty principle;    Orthonormal bases;    Time-frequency concentration;   

DOI  :  10.1016/j.jat.2014.10.008

来源: Elsevier

【 摘 要 】

The aim of this paper is to prove a quantitative extension of Shapiro's result on the time frequency concentration of orthonormal sequences in 4(I14). More precisely, we prove that, if {gon}n+cxij is an orthonormal sequence in L, (R+), then for all N > 0 E Oxcon 02q, + Il7-(a(con)0.L.0 > 2(N 1)(N +1+ a), n=0 and the equality is attained for the sequence of Laguerre functions. Particularly if the elements of an orthonormal sequence and their Fourier Bessel transforms (or Hankel transforms) have uniformly bounded dispersions then the sequence is finite. Moreover we prove the following strong uncertainty principle for bases for L2, (R+), that is if {yon}04 1 is an orthonormal basis for L, (R+) and s > 0, then sup( xs C9n112,110-1c6(C9n)112L0 = +00. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free