A short elementary proof of the Gearhart-Pr\"uss theorem for bounded semigroups
Filippo Dell'Oro, David Seifert
TL;DR
This paper provides a concise and elementary proof of the Gearhart-Prüss theorem, which characterizes the stability of bounded $C_0$-semigroups on Hilbert spaces.
Contribution
The authors offer a simplified, elementary proof of the Gearhart-Prüss theorem, enhancing understanding and accessibility of this fundamental result.
Findings
Elementary proof of the Gearhart-Prüss theorem
Clarification of stability criteria for bounded semigroups
Improved pedagogical approach to semigroup theory
Abstract
We present a short elementary proof of the Gearhart-Pr\"uss theorem for bounded -semigroups on Hilbert spaces.
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Taxonomy
TopicsFunctional Equations Stability Results · Advanced Banach Space Theory · Advanced Operator Algebra Research