On the lower Riesz basis bound of exponential systems over an interval
Thibaud Alemany, Shahaf Nitzan
TL;DR
This paper revisits classical results on Riesz bases of exponential systems, improving bounds on their stability and zero distribution through refined analysis of Pavlov's characterization.
Contribution
It provides improved estimates for lower Riesz basis bounds in exponential systems, enhancing understanding of stability under perturbations and zero distribution.
Findings
Enhanced bounds for Riesz basis stability
Refined estimates for zeroes of sine-type functions
Improved understanding of exponential system perturbations
Abstract
We revisit Pavlov's characterization for Riesz bases of exponentials and study the corresponding lower Riesz basis bounds. In particular, this approach allows us to improve on known estimates for the bounds in Avdonin's theorem regarding average perturbations, and Levin's theorem regarding zeroes of sine-type functions.
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Taxonomy
TopicsControl Systems and Identification · Mathematical Control Systems and Analysis · Stability and Control of Uncertain Systems