相关论文: The inhomogeneous Cauchy-Riemann equation for weig…
We study the inhomogeneous Cauchy-Riemann equation on spaces $\mathcal{EV}(\Omega,E)$ of weighted $\mathcal{C}^{\infty}$-smooth $E$-valued functions on an open set $\Omega\subset\mathbb{R}^{2}$ whose growth on strips along the real axis is…
We derive sufficient conditions for the surjectivity of the Cauchy-Riemann operator $\overline{\partial}$ between spaces of weighted smooth Fr\'echet-valued functions. This is done by establishing an analog of H\"ormander's theorem on the…
We study the linear topological invariant $(\Omega)$ for a class of Fr\'echet spaces of holomorphic functions of rapid decay on strip-like domains in the complex plane, defined via weight function systems. We obtain a complete…
We study the surjectivity of the Cauchy-Riemann and Laplace operators on certain weighted spaces of smooth functions of rapid decay on strip-like domains in the complex plane that are defined via weight function systems. We fully…
We introduce a new class $\mathcal{FV}(\Omega,E)$ of spaces of weighted functions on a set $\Omega$ with values in a locally convex Hausdorff space $E$ which covers many classical spaces of vector-valued functions like continuous, smooth,…
This habilitation thesis centres on linearisation of vector-valued functions which means that vector-valued functions are represented by continuous linear operators. The first question we face is which vector-valued functions may be…
In this paper we study the problem of extending functions with values in a locally convex Hausdorff space $E$ over a field $\mathbb{K}$, which have weak extensions in a weighted Banach space $\mathcal{F}\nu(\Omega,\mathbb{K})$ of…
We give a unified approach to handle the problem of extending functions with values in a locally convex Hausdorff space $E$ over a field $\mathbb{K}$, which have weak extensions in a space $\mathcal{F}(\Omega,\mathbb{K})$ of scalar-valued…
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 space $E$ over $\mathbb{C}$. Most of the literature on…
We establish the condition $(\Omega)$ for smooth kernels of various types of convolution and differential operators. By the $(DN)$-$(\Omega)$ splitting theorem of Vogt and Wagner, this implies that these operators are surjective on the…
We study spaces $\mathcal{CV}^{k}(\Omega,E)$ of $k$-times continuously partially differentiable functions on an open set $\Omega\subset\mathbb{R}^{d}$ with values in a locally convex Hausdorff space $E$. The space…
The aim of this paper is to give an extension of the improved Sobolev embedding theorem for single-valued functions to the case of vector-valued functions which is involved with the three-dimensional massless Dirac operator together with…
We prove that the spaces of smooth and ultradifferentiable vectors associated with a representation of a real Lie group on a Fr\'{e}chet space $E$ are quasinormable if $E$ is so. A similar result is shown to hold for the linear topological…
The $k$-Cauchy-Fueter operators, $k=0,1,\ldots$, are quaternionic counterparts of the Cauchy-Riemann operator in the theory of several complex variables. The weighted $L^2$ method to solve Cauchy-Riemann equation is applied to find the…
In this paper, we investigate analytic divergence-free vector fields and vector fields admitting a Jacobi multiplier on $n$-dimensional Riemannian manifolds. We first introduce a functional acting on the space of divergence-free vector…
Given an action of a Lie group on a smooth manifold, we discuss the induced action on the Hochschild cohomology of smooth functions, and notions of invariance on this space. Depending on whether one considers invariance of cochains or…
The algebra of smooth translation-invariant valuations on convex bodies, introduced by S.Alesker in the early 2000s, was in part proved and in part conjectured to satisfy properties formally analogous to those of the cohomology ring of a…
A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary…
The $k$-Cauchy-Fueter operator $ D_0^{(k) } $ on one dimensional quaternionic space $\mathbb{H}$ is the Euclidean version of helicity $\frac k 2$ massless field operator on the Minkowski space in physics. The $k$-Cauchy-Fueter equation for…
The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy Mean Value Theorem is taken at a point which has a well-determined position in the interval. As an application of this…