On the Gabor frame set for compactly supported continuous functions
Functional Analysis
2016-02-19 v1
Abstract
We identify a class of continuous compactly supported functions for which the known part of the Gabor frame set can be extended. At least for functions with support on an interval of length two, the curve determining the set touches the known obstructions. Easy verifiable sufficient conditions for a function to belong to the class are derived, and it is shown that the B-splines as well as certain "continuous and truncated" versions of several classical functions (e.g., the Gaussian and the two-sided exponential function) belong to the class. The sufficient conditions for the frame property guarantees the existence of a dual window with a prescribed size of the support.
Keywords
Cite
@article{arxiv.1602.05717,
title = {On the Gabor frame set for compactly supported continuous functions},
author = {Ole Christensen and Hong Oh Kim and Rae Young Kim},
journal= {arXiv preprint arXiv:1602.05717},
year = {2016}
}
Comments
in Journal of Inequalities and Applications, 2016