[PDF.12cq] The abc-Problem for Gabor Systems (Memoirs of the American Mathematical Society)

The abc-Problem for Gabor Systems (Memoirs of the American Mathematical Society)

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 |  2016-10-23 | Original language:English |  10.00 x7.00 x.25l, | File type: PDF | 99 pages

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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.

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 invar...

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