Tiling functions and Gabor orthonormal basis
Classical Analysis and ODEs
2017-04-11 v1
Abstract
We study the existence of Gabor orthonormal bases with window the characteristic function of the set W=[0,a] U [b+a, b+1] of measure 1, with a, b>0. By the symmetries of the problem, we can restrict our attention to the case a<=1/2. We prove that either if a<1/2 or (a=1/2 and b>= 1/2) there exist such Gabor orthonormal bases, with window the characteristic function of the set W, if and only if W tiles the line. Furthermore, in both cases, we completely describe the structure of the set of time-frequency shifts associated to these bases
Keywords
Cite
@article{arxiv.1704.02831,
title = {Tiling functions and Gabor orthonormal basis},
author = {Elona Agora and Jorge Antezana and Mihail N. Kolountzakis},
journal= {arXiv preprint arXiv:1704.02831},
year = {2017}
}
Comments
29 pages, 12 figures