Taiwanese Journal of Mathematics

THE ART OF FRAME THEORY

Peter G. Casazza

Full-text: Open access

Abstract

The theory of frames for a Hilbert space plays a fundamental role in signal processing, image processing, data compression, sampling theory and more, as well as being a fruitful area of research in abstract mathematics. In this “tutorial” on abstract frame theory, we will try to point out the major directions of research in abstract frame theory and give some sample techniques from each of the areas. We will also bring out some of the important open questions, discuss some of the limitations of the existing theory, and point to some new directions for research.

Article information

Source
Taiwanese J. Math., Volume 4, Number 2 (2000), 129-201.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407227

Digital Object Identifier
doi:10.11650/twjm/1500407227

Mathematical Reviews number (MathSciNet)
MR1757401

Zentralblatt MATH identifier
0966.42022

Subjects
Primary: 42C15: General harmonic expansions, frames 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Keywords
(Gabor) frame Fourier series Hilbert space linear operator perturbation Riesz basis Weyl-Heisenberg system

Citation

Casazza, Peter G. THE ART OF FRAME THEORY. Taiwanese J. Math. 4 (2000), no. 2, 129--201. doi:10.11650/twjm/1500407227. https://projecteuclid.org/euclid.twjm/1500407227


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