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

Dai, Xin-Rong; Sun, Qiyu

Softcover

ISBN 10: 1470420155 ISBN 13: 9781470420154

Publisher: American Mathematical Society, 2016

Synopsis

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.

About this title

About the Author

Xin-Rong Dai, Sun Yat-sen University, Guangzhou, China.

Qiyu Sun, University of Central Florida, Orlando, Florida, USA.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2016
• Language: English
• ISBN 10: 1470420155
• ISBN 13: 9781470420154
• Binding: Paperback
• Number of pages: 99