Synopsis
A longstanding problem in Gabor theory is to identify time-frequency shifting lattices $amathbbZtimes bmathbbZ$ and ideal window functions $chiI$ on intervals $I$ of length $c$ such that $e-2pi i n bt chiI(t- m a): (m, n)in mathbbZtimes mathbbZ$ are Gabor frames for the space of all square-integrable functions on the real line. In this paper, the authors create a time-domain approach for Gabor frames, introduce novel techniques involving invariant sets of non-contractive and non-measure-preserving transformations on the line, and provide a complete answer to the above $abc$-problem for Gabor systems.
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About the Author
Xin-Rong Dai, Sun Yat-sen University, Guangzhou, China.Qiyu Sun, University of Central Florida, Orlando, Florida, USA.
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The abc-problem for Gabor systems. Memoirs of the American Mathematical Society; Bd. volume 244, number 1152 (1st of 4 numbers).
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Providence, American Mathematical Society, 2016
ISBN 10: 1470420155
ISBN 13: 9781470420154
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