Semi-uniform stability of semigroups and their cogenerators

Andrew Pritchard (University of Newcastle)

Thursday 27th February 16:00-17:00 Maths 311B

Abstract

Semi-uniform stability for a strongly continuous semigroup refers to the stability of classical solutions of a linear evolution equation. The cogenerator of a strongly continuous semigroup is a bounded linear operator defined as the Cayley transform of the generator. In this talk, I will present some results relating the (quantified) stability of strongly continuous semigroups with that of the discrete semigroup given by powers of the cogenerator. These results are obtained through two distinct approaches. The first approach is based on resolvent estimates and uses a quantified version of the classical Katznelson-Tzafriri theorem. The second approach is based on an integrability condition and the boundedness of a certain vector-valued integral transform.

This talk is based on joint work with David Seifert.

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