81 citations · 350 across the 28 of their papers we have counts for
28 papers
A short elementary proof of the Gearhart-Prüss theorem for bounded semigroups
Filippo Dell'Oro, David Seifert
We present a short elementary proof of the Gearhart-Prüss theorem for bounded -semigroups on Hilbert spaces.
Some developments around the Katznelson-Tzafriri theorem
Charles Batty, David Seifert
This paper is a survey article on developments arising from a theorem proved by Katznelson and Tzafriri in 1986 showing that if is a power-b…
A continuous-parameter Katznelson-Tzafriri theorem for algebras of analytic functions
Charles Batty, David Seifert
We prove a continuous-parameter version of the recent theorem of Katznelson-Tzafiri type for power-bounded operators which have a bounded calculus for analytic Besov functions. We…
A Katznelson-Tzafriri theorem for analytic Besov functions of operators
Charles Batty, David Seifert
Let be a power-bounded operator on a Banach space , be a Banach algebra of bounded holomorphic functions on the unit disc , and assume that there i…
Optimal decay for a wave-heat system with Coleman-Gurtin thermal law
Filippo Dell'Oro, Lassi Paunonen, David Seifert
We study the long-term behaviour of solutions to a one-dimensional coupled wave-heat system with Coleman-Gurtin thermal law. Our approach is based on the asymptotic theory of …
Semi-uniform stability of operator semigroups and energy decay of damped waves
R. Chill, D. Seifert, Y. Tomilov
Only in the last fifteen years or so has the notion of semi-uniform stability, which lies between exponential stability and strong stability, become part of the asymptotic theory o…
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…
Non-uniform Stability of Damped Contraction Semigroups
Ralph Chill, Lassi Paunonen, David Seifert +2
We investigate the stability properties of strongly continuous semigroups generated by operators of the form , where is a generator of a contraction semigroup and $B…
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…
Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry
Mustapha Mokhtar-Kharroubi, David Seifert
This work deals with free transport equations with partly diffuse stochastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in sp…
Optimal rates of decay for operator semigroups on Hilbert spaces
Jan Rozendaal, David Seifert, Reinhard Stahn
We investigate rates of decay for -semigroups on Hilbert spaces under assumptions on the resolvent growth of the semigroup generator. Our main results show that one obtains th…
Non-optimality of the Greedy Algorithm for subspace orderings in the method of alternating projections
Oscar Darwin, Aashraya Jha, Souktik Roy +3
The method of alternating projections involves projecting an element of a Hilbert space cyclically onto a collection of closed subspaces. It is known that the resulting sequence al…
Quantified asymptotic behaviour of Banach space operators and applications to iterative projection methods
Catalin Badea, David Seifert
We present an extension of our earlier work [Ritt operators and convergence in the method of alternating projections, J. Approx. Theory, 205:133-148, 2016] by proving a general asy…
Asymptotics for periodic systems
Lassi Paunonen, David Seifert
This paper investigates the asymptotic behaviour of solutions of periodic evolution equations. Starting with a general result concerning the quantified asymptotic behaviour of peri…
Asymptotic behaviour of coupled systems in discrete and continuous time
L. Paunonen, D. Seifert
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those init…
Asymptotic behaviour in the robot rendezvous problem
L. Paunonen, D. Seifert
We present a non-technical overview of the results obtained by the authors (2015) concerning the so-called robot rendezvous problem studied by Feintuch and Francis (2012). In parti…
Asymptotics for infinite systems of differential equations
Lassi Paunonen, David Seifert
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of ordinary differential equations. In particular, we use results from ergodic theory and…
Ritt operators and convergence in the method of alternating projections
Catalin Badea, David Seifert
Given closed subspaces of a Hilbert space , let denote the orthogonal projection onto , . It is known that the sequence …
Optimal energy decay in a one-dimensional coupled wave-heat system
C. J. K. Batty, L. Paunonen, D. Seifert
We study a simple one-dimensional coupled wave-heat system and obtain a sharp estimate for the rate of energy decay of classical solutions. Our approach is based on the asymptotic…
A quantified Tauberian theorem for sequences
David Seifert
The main result of this paper is a quantified version of Ingham's Tauberian theorem for bounded vector-valued sequences rather than functions. It gives an estimate on the rate of d…