174 citations · 370 across the 32 of their papers we have counts for
32 papers
On linearisation and existence of preduals
Karsten Kruse
We study the problem of existence of preduals of locally convex Hausdorff spaces. We derive necessary and sufficient conditions for the existence of a predual with certain properti…
On linearisation, existence and uniqueness of preduals: The isometric case
Karsten Kruse
We study the problem of existence and uniqueness of isometric Banach preduals of a Banach space. We derive necessary and sufficient conditions for the existence of an isometric Ban…
On linearisation and uniqueness of preduals
Karsten Kruse
We study strong linearisations and the uniqueness of preduals of locally convex Hausdorff spaces of scalar-valued functions. Strong linearisations are special preduals. A locally c…
On vector-valued functions and the -product
Karsten Kruse
This habilitation thesis centres on linearisation of vector-valued functions which means that vector-valued functions are represented by continuous linear operators. The first ques…
Weighted composition semigroups on spaces of continuous functions and their subspaces
Karsten Kruse
This paper is dedicated to weighted composition semigroups on spaces of continuous functions and their subspaces. We consider semigroups induced by semiflows and semicocycles on Ba…
Mixed topologies on Saks spaces of vector-valued functions
Karsten Kruse
We study Saks spaces of functions with values in a normed space and the associated mixed topologies. We are interested in properties of such Saks spaces and mixed topologies which…
A note on the Lumer--Phillips theorem for bi-continuous semigroups
Karsten Kruse, Christian Seifert
Given a Banach space and an additional coarser Hausdorff locally convex topology on we characterise the generators of -bi-continuous semigroups in the spirit of the…
Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups
Karsten Kruse, Christian Seifert
We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time by taking in…
Sun dual theory for bi-continuous semigroups
Karsten Kruse, Felix L. Schwenninger
The sun dual space corresponding to a strongly continuous semigroup is a known concept when dealing with dual semigroups, which are in general only weak-continuous. In this pap…
The abstract Cauchy problem in locally convex spaces
Karsten Kruse
We derive sufficient criteria for the uniqueness and existence of solutions of the abstract Cauchy problem in locally convex Hausdorff spaces. Our approach is based on a suitable n…
On equicontinuity and tightness of bi-continuous semigroups
Karsten Kruse, Felix L. Schwenninger
In contrast to classical strongly continuous semigroups, the study of bi-continuous semigroups comes with some freedom in the properties of the associated locally convex topology.…
Asymptotic Fourier and Laplace transforms for vector-valued hyperfunctions
Karsten Kruse
We study Fourier and Laplace transforms for Fourier hyperfunctions with values in a complex locally convex Hausdorff space. Since any hyperfunction with values in a wide class of l…
Exponential single server queues in an interactive random environment
Sonja Otten, Ruslan Krenzler, Hans Daduna +1
We consider exponential single server queues with state-dependent arrival and service rates which evolve under influences of external environments. The transitions of the queues ar…
On the solvability of the matrix equation
Karsten Kruse
The treated matrix equation in this short note has its origin in a modelling approach to describe the nonlinear time-dependent mechanical behaviour o…
Lost-customers approximation of semi-open queueing networks with backordering -- An application to minimise the number of robots in robotic mobile fulfilment systems
Sonja Otten, Ruslan Krenzler, Lin Xie +2
We consider a semi-open queueing network (SOQN), where a customer requires exactly one resource from the resource pool for service. If there is a resource available, the customer i…
Vector-valued Fourier hyperfunctions and boundary values
Karsten Kruse
This work is dedicated to the development of the theory of Fourier hyperfunctions in one variable with values in a complex non-necessarily metrisable locally convex Hausdorff space…
Vector-valued holomorphic functions in several variables
Karsten Kruse
In the present paper we give some explicit proofs for folklore theorems on holomorphic functions in several variables with values in a locally complete locally convex Hausdorff spa…
Extension of vector-valued functions and weak-strong principles for differentiable functions of finite order
Karsten Kruse
In this paper we study the problem of extending functions with values in a locally convex Hausdorff space over a field , which have weak extensions in a weighted Ba…
Parameter dependence of solutions of the Cauchy-Riemann equation on spaces of weighted smooth functions
Karsten Kruse
We study the inhomogeneous Cauchy-Riemann equation on spaces of weighted -smooth -valued functions on an open set $Ω\subset\mathbb{R}^{…
The inhomogeneous Cauchy-Riemann equation for weighted smooth vector-valued functions on strips with holes
Karsten Kruse
This paper is dedicated to the question of surjectivity of the Cauchy-Riemann operator on spaces of -smooth vector-valued functions whose…
Surjectivity of the -operator between weighted spaces of smooth vector-valued functions
Karsten Kruse
We derive sufficient conditions for the surjectivity of the Cauchy-Riemann operator between spaces of weighted smooth Fréchet-valued functions. This is done b…
On the nuclearity of weighted spaces of smooth functions
Karsten Kruse
Nuclearity plays an important role for the Schwartz kernel theorem to hold and in transferring the surjectivity of a linear partial differential operator from scalar-valued to vect…
Extension of vector-valued functions and sequence space representation
Karsten Kruse
We give a unified approach to handle the problem of extending functions with values in a locally convex Hausdorff space over a field , which have weak extensions in…
The approximation property for weighted spaces of differentiable functions
Karsten Kruse
We study spaces of -times continuously partially differentiable functions on an open set with values in a locally convex Hausdor…