On the Gabor frame set for compactly supported continuous functions

Ole Christensen, Hong Oh Kim, Rae Young Kim

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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 BN, N≥2, and 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.
Original languageEnglish
Article number94
JournalJournal of Inequalities and Applications
Volume2016
Number of pages17
ISSN1025-5834
DOIs
Publication statusPublished - 2016

Bibliographical note

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Keywords

  • Gabor frames
  • Frame set
  • B-splines

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