The $abc$-Problem for Gabor Systems

The $abc$-Problem for Gabor Systems
Author :
Publisher : American Mathematical Soc.
Total Pages : 116
Release :
ISBN-10 : 9781470420154
ISBN-13 : 1470420155
Rating : 4/5 (54 Downloads)

Book Synopsis The $abc$-Problem for Gabor Systems by : Xin-Rong Dai

Download or read book The $abc$-Problem for Gabor Systems written by Xin-Rong Dai and published by American Mathematical Soc.. This book was released on 2016-10-05 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: A longstanding problem in Gabor theory is to identify time-frequency shifting lattices aZ×bZ and ideal window functions χI on intervals I of length c such that {e−2πinbtχI(t−ma): (m,n)∈Z×Z} 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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