6 papers
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…
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…
Optimal energy decay in a one-dimensional wave-heat system with infinite heat part
Abraham C. S. Ng, David Seifert
Using recent results in the theory of -semigroups due to Batty, Chill and Tomilov (J. Eur. Math. Soc. 18(4):853-929, 2016) we study energy decay in a one-dimensional coupled w…
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…
An abstract approach to optimal decay of functions and operator semigroups
Gregory Debruyne, David Seifert
We provide a new and significantly shorter optimality proof of recent quantified Tauberian theorems, both in the setting of vector-valued functions and of -semigroups, and in…
Optimal energy decay for the wave-heat system on a rectangular domain
Charles Batty, Lassi Paunonen, David Seifert
We study the rate of energy decay for solutions of a coupled wave-heat system on a rectangular domain. Using techniques from the theory of -semigroups, and in particular a wel…