On Gabor frames generated by sign-changing windows and B-splines

Ole Christensen, Hong Oh Kim, Rae Young Kim

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

For a class of compactly supported windows we characterize the frame property for a Gabor system {EmbTnag}m,nZ, for translation parameters a belonging to a certain range depending on the support size. We show that the obstructions to the frame property are located on a countable number of "curves." For functions that are positive on the interior of the support these obstructions do not appear, and the considered region in the (a,b) plane is fully contained in the frame set. In particular this confirms a recent conjecture about B-splines by Gröchenig in that particular region. We prove that the full conjecture is true if it can be proved in a certain "hyperbolic strip."
Original languageEnglish
JournalApplied and Computational Harmonic Analysis
Volume39
Issue number3
Pages (from-to)534-544
ISSN1063-5203
DOIs
Publication statusPublished - 2015

Keywords

  • Gabor frames
  • Frame set
  • B-splines

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