6 papers
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…
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…
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}^{…
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…
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…
Series representations in spaces of vector-valued functions via Schauder decompositions
Karsten Kruse
It is a classical result that every -valued holomorphic function has a local power series representation. This even remains true for holomorphic functions with values i…