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Non-symmetric convex polytopes and Gabor orthonormal bases


Authors: Randolf Chung and Chun-kit Lai
Journal: Proc. Amer. Math. Soc. 146 (2018), 5147-5155
MSC (2010): Primary 42C15, 52B11
DOI: https://doi.org/10.1090/proc/14183
Published electronically: September 4, 2018
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Abstract: In this paper, we show that non-symmetric convex polytopes cannot serve as a window function to produce a Gabor orthonormal basis by any time-frequency sets.


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Additional Information

Randolf Chung
Affiliation: Department of Mathematics, San Francisco State University, San Francisco, California 94132
Email: university@jeongjh.com

Chun-kit Lai
Affiliation: Department of Mathematics, San Francisco State University, San Francisco, California 94132
Email: cklai@sfsu.edu

DOI: https://doi.org/10.1090/proc/14183
Keywords: Gabor orthonormal bases, polytope, spectral sets, tilings
Received by editor(s): November 26, 2017
Published electronically: September 4, 2018
Additional Notes: This work was an undergraduate research project in 2015-16 supported by the Office of Research and Sponsorship Programs (ORSP) at San Francisco State University (Grant No. ST 659).
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2018 American Mathematical Society

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