The Abc-Problem For Gabor Systems

Keywords

Abc problem for Gabor systems; Ergodic theorem; Gabor frames; Infinite matrices; Piecewise linear transformation; Sampling; Shift invariant spaces

Abstract

A longstanding problem in Gabor theory is to identify time frequency shifting lattices aZ × bZ and ideal window functions χI on intervals I of length c such that {equation presented} : {equation presented} are Gabor frames for the space of all square integrable functions on the real line. In this paper, we create a timedomain 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.

Publication Date

11-1-2016

Publication Title

Memoirs of the American Mathematical Society

Volume

244

Issue

1152

Number of Pages

1-116

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/memo/1152

Socpus ID

84989940446 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84989940446

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