Two Aspects of the Donoho-Stark Uncertainty Principle

TL;DR

This paper introduces new forms of the uncertainty principle involving localization operators, epsilon-concentration, and standard deviation, improving classical bounds with more general and signal-dependent estimates.

Contribution

It presents novel uncertainty bounds that enhance the Donoho-Stark estimate by incorporating localization operators and signal-specific parameters.

Findings

Improved lower bounds on uncertainty measures

Enhanced classical Donoho-Stark estimates

Bounds dependent on signal properties

Abstract

We present some forms of uncertainty principle which involve in a new way localization operators, the concept of $\varepsilon$-concentration and the standard deviation of $L^2$ functions. We show how our results improve the classical Donoho-Stark estimate in two different aspects: a better general lower bound and a lower bound in dependence on the signal itself.