Invertibility of Positive Toeplitz Operators and Associated Uncertainty Principle

TL;DR

This paper investigates the invertibility and compactness of positive Toeplitz operators linked to continuous frames, providing characterizations and uncertainty principles relevant to signal analysis and operator theory.

Contribution

It offers new characterizations of compactness and invertibility for Toeplitz operators and establishes uncertainty principles for related transforms.

Findings

Characterization of compactness of affine and Weyl-Heisenberg localization operators

Criteria for invertibility of positive Toeplitz operators

Uncertainty principles for associated transforms

Abstract

We study invertibility and compactness of positive Toeplitz operators associated to a continuous Parseval frame on a Hilbert space. As applications, we characterize compactness of affine and Weyl-Heisenberg localization operators as well as give uncertainty principles for the associated transforms.