The abc-Problem for Gabor Systems

Ebook Details

Authors

Xin-rong Dai, Qiyu Sun

Year 2016
Pages 99
Publisher Amer Mathematical Society
Language en
ISBN 9781470420154
File Size 1.07 MB
File Format PDF
Download Counter 106
Amazon Link
Google Book Link

Ebook 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.