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The ABC - Problem for Gabor Systems: 1152 (Memoirs of the American Mathematical Society)

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Description

About the Author Xin-Rong Dai, Sun Yat-sen University, Guangzhou, China.Qiyu Sun, University of Central Florida, Orlando, Florida, USA. Product Description A longstanding problem in Gabor theory is to identify time-frequency shifting lattices $a\mathbb{Z}\times b\mathbb{Z}$ and ideal window functions $\chi_I$ on intervals $I$ of length $c$ such that $\{e^{-2\pi i n bt} \chi_I(t- m a):\ (m, n)\in \mathbb{Z}\times \mathbb{Z}\}$ 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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paperback
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Amazon UK
Release Date
30 October 2016
Listed Since
17 August 2016

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