相关论文: Normed domains of holomorphy

Let $\mu$ be a positive finite Borel measure on $[0,1).$ Ces\`aro-type operators $C_{\mu}$ when acting on weighted spaces of holomorphic functions are investigated. In the case of bounded holomorphic functions on the unit disc we prove that…

We describe the norming sets for the space of global holomorphic sections to a $k$-power of a positive holomorphic line bundle on a compact complex manifold $X$. We characterize in metric terms the sequence of measurable subsets…

In this article, we introduce the concept of weakly uniquely stationary representations. This framework enables us to investigate the complementability of closed subspaces within the context of continuous cohomology with coeffcients in…

The problem of characterizing normed ordered spaces which admit a representation in the algebraic, order and norm sense as a subspace of $C(X)$, the space of all continuous functions on a compact Hausdorff space is a classical problem that…

We study the fixed point sets of holomorphic self-maps of a bounded domain in ${\Bbb C}^n$. Specifically we investigate the least number of fixed points in general position in the domain that forces any automorphism (or endomorphism) to be…

The classical integral representation formulas for holomorphic functions defined on pseudoconvex domains in Stein manifolds play an important role in the constructive theory of functions of several complex variables. In this paper we…

We modify the very well known theory of normed spaces $(E, \norm)$ within functional analysis by considering a sequence $(\norm_n : n\in\N)$ of norms, where $\norm_n$ is defined on the product space $E^n$ for each $n\in\N$. Our theory is…

For $D$, $D'$ analytic polyhedra in $C^n$, it is proven that a biholomorphic mapping $f\colon D\to D'$ extends holomorphically to a dense boundary subset under certain condition of general position. This result is also extended to a more…

In the first half of twentieth century the theory of complex analytic functions and of their zerosets was fully developed. The definition of holomorphic function has a local nature. Germs of holomorphic functions form a distinguished…

We generalise the Denjoy-Wolff theorem for a fixed-point free holomorphic self-map on the complex unit disc to bounded symmetric domains of finite rank in complex Banach spaces.

We are concerned with the analysis of a mean field type equation and its linearization, which is a nonlocal operator, for which we estimate the number of nodal domains for the radial eigenfunctions and the related uniqueness properties.

Among plenty of applications, low-dimensional homogeneous spaces appear in cosmological models as both, classical factor spaces of multidimensional geometry and minisuperspaces in canonical quantization. Here a new tool to restrict their…

We introduce a continuous domain for function spaces over topological spaces which are not core-compact. Notable examples of such topological spaces include the real line with the upper limit topology, which is used in solution of initial…

There exist several interesting results in the literature on subnormal operator tuples having their spectral properties tied to the geometry of strictly pseudoconvex domains or to that of bounded symmetric domains in $\C^n$. We introduce a…

We consider the 1-harmonic flow of maps from a bounded domain into a submanifold of a Euclidean space, i.e. the gradient flow of the total variation functional restricted to maps taking values in the manifold. We restrict ourselves to…

We present a construction that allows us to define a limit object of Banach space decorated graph sequences in a generalized homomorphism density sense. This general functional analytic framework provides a universal language for various…

We prove a suite of results classifying holomorphic maps between configuration spaces of Riemann surfaces; we consider both the ordered and unordered setting as well as the cases of genus zero, one, and at least two. We give a complete…

A domain $G\subset \bar\mathbb C$ is the domain of holomorphy of the generating function of a P\'olya frequency sequence of order $r$ if and only if it satisfies the following conditions: (A) $G$ contains the point $z=0$, (B) $G$ is…

We give a complete characterization of those $f: [0,1] \to X$ (where $X$ is a Banach space which admits an equivalent Fr\'echet smooth norm) which allow an equivalent $C^2$ parametrization. For $X=\R$, a characterization is well-known.…

We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the existence of symmetric linear functionals. Many of the presented…