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math.FA2020
Optimal rates of decay in the Katznelson-Tzafriri theorem for operators on Hilbert spaces
Abraham C. S. Ng, David Seifert
The Katznelson-Tzafriri theorem is a central result in the asymptotic theory of discrete operator semigroups. It states that for a power-bounded operator on a Banach space we h…
math.FA2019
Asymptotics and approximation of large systems of ordinary differential equations
Lassi Paunonen, David Seifert
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-call…
math.FA2018
Optimality of the quantified Ingham-Karamata theorem for operator semigroups with general resolvent growth
Gregory Debruyne, David Seifert
We prove that a general version of the quantified Ingham-Karamata theorem for -semigroups is sharp under mild conditions on the resolvent growth, thus generalising the results…