3 citations · 5 across the 8 of their papers we have counts for
10 papers
On the Cyclicity Conjecture
Alexander Dobrick
We prove that the peripheral spectrum of every positive operator on a complex Banach lattice is cyclic, thereby resolving the cyclicity conjecture without additional growth assumpt…
Individual and Uniform Eventual Positivity of Self-Adjoint Semigroups
Alexander Dobrick
We construct a real self-adjoint semigroup on an -space which is individually eventually strongly positive with respect to a strictly positive vector, but whose operators f…
Banach's principle in vector lattices
Alexander Dobrick
We develop an abstract Banach principle in vector lattices and apply it to obtain lattice-theoretic versions of the individual and maximal ergodic theorems, without recourse to any…
Well-posedness and long-term behaviour of buffered flows in infinite networks
Alexander Dobrick, Florian G. Martin
We consider a transport problem on an infinite metric graph and discuss its well-posedness and long-term behaviour under the condition that the mass flow is buffered in at least on…
Ultra Feller operators from a functional analytic perspective
Alexander Dobrick, Julian Hölz, Markus Kunze
It is a widely acknowledged fact that the product of two positive strong Feller operators on a Polish space enjoys the ultra Feller property. We present a functional analytic p…
Uniform convergence of solutions to stochastic hybrid models of gene regulatory networks
Alexander Dobrick, Julian Hölz
In a recent paper by Kurasov, Lück, Mugnolo and Wolf, a hybrid gene regulatory network was proposed to model gene expression dynamics by using a stochastic system of coupled partia…
Convergence to equilibrium for linear parabolic systems coupled by matrix-valued potentials
Alexander Dobrick, Jochen Glück
We consider systems of parabolic linear equations, subject to Neumann boundary conditions on bounded domains in , that are coupled by a matrix-valued potential , a…
A monotone convergence theorem for strong Feller semigroups
Christian Budde, Alexander Dobrick, Jochen Glück +1
For an increasing sequence of one-parameter semigroups of sub Markovian kernel operators over a Polish space, we study the limit semigroup and prove sufficient conditions f…
On the asymptotic behaviour of semigroups for flows in infinite networks
Alexander Dobrick
We study transport processes on infinite networks. The solution of these processes can be modeled by an operator semigroup on a suitable Banach space. Classically, such semigroups…
Uniform convergence of operator semigroups without time regularity
Alexander Dobrick, Jochen Glück
When we are interested in the long-term behaviour of solutions to linear evolution equations, a large variety of techniques from the theory of -semigroups is at our disposal.…