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.
| ISBN: | 9781470420154 |
| Publication date: | 30th October 2016 |
| Author: | XinRong Dai, Qiyu Sun |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 99 pages |
| Series: | Memoirs of the American Mathematical Society |
| Genres: |
Functional analysis and transforms |
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.
The Abc-Problem for Gabor Systems features in the following genres: Functional analysis and transforms
The Abc-Problem for Gabor Systems is available in Paperback
The Abc-Problem for Gabor Systems was written by XinRong Dai, Qiyu Sun and published by American Mathematical Society
The Abc-Problem for Gabor Systems has 99 pages
Yes it is part of Memoirs of the American Mathematical Society series