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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Irregular Gabor frames and their stability


Authors: Wenchang Sun and Xingwei Zhou
Journal: Proc. Amer. Math. Soc. 131 (2003), 2883-2893
MSC (2000): Primary 41A58, 42C15, 42C40
Published electronically: December 30, 2002
MathSciNet review: 1974346
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Abstract: In this paper we give sufficient conditions for irregular Gabor systems to be frames. We show that for a large class of window functions, every relatively uniformly discrete sequence in $\mathbb R^2$ with sufficiently high density will generate a Gabor frame. Explicit frame bounds are given. We also study the stability of irregular Gabor frames and show that every Gabor frame with arbitrary time-frequency parameters is stable if the window function is nice enough. Explicit stability bounds are given.


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Additional Information

Wenchang Sun
Affiliation: Department of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
Email: sunwch@nankai.edu.cn

Xingwei Zhou
Affiliation: Department of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
Email: xwzhou@nankai.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06931-9
PII: S 0002-9939(02)06931-9
Keywords: Gabor frames, Weyl-Heisenberg frames, stability
Received by editor(s): August 29, 2001
Received by editor(s) in revised form: March 2, 2002, and April 11, 2002
Published electronically: December 30, 2002
Additional Notes: This work was supported by the National Natural Science Foundation of China (Grant Nos. 10171050 and 10201014), the Mathematical Tianyuan Foundation (Grant No. TY10126007), the Research Fund for the Doctoral Program of Higher Education, and the Liuhui Center for Applied Mathematics.
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society