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

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• 作者：Ole Christensen^a ; ^{ochr@dtu.dk" class="auth_mail" title="E-mail the corresponding author} ; Hong Oh Kim^b ; ^{hkim2031@unist.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Rae Young Kim^c ; ^{rykim@ynu.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Gabor frames ; Frame set ; B-splines
• 刊名：Applied and Computational Harmonic Analysis
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：39
• 期：3
• 页码：534-544
• 全文大小：412 K

文摘

For a class of compactly supported windows we characterize the frame property for a Gabor system {E_mbT_nag}_m,n∈Z${\{E_{mb}{T}_{na}g\}}_{m,n\in \mathbb{Z}}$, 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)$(a,b)$ 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.”