相关论文: An extension theorem for separately meromorphic fu…

Let B be the open unit ball in C^2 and let a, b, c be three points in C^2 which do not lie in a complex line, such that the complex line through a and b meets B and such that <a|b> is different from 1 if one of the points a, b is in B and…

We consider a space of infinitely smooth functions on an unbounded closed convex set in ${\mathbb R}^n$. It is shown that each function of this space can be extended to an entire function in ${\mathbb C}^n$ satisfying some prescribed growth…

We investigate the question of existence of plurisubharmonic defining functions for smoothly bounded, pseudoconvex domains in $\mathbb{C}^2$. In particular, we construct a family of simple counterexamples to the existence of…

Given a pseudoconvex domain D in C^N, N>1, we prove that there is a holomorphic function f on D such that the lengths of paths p: [0,1]--> D along which Re f is bounded above, with p(0) fixed, grow arbitrarily fast as p(1)--> bD. A…

Let A be a domain of the boundary of a strictly pseudoconvex domain \Omega of C^n and M a smooth, closed, maximally complex submanifold of A. We find a subdomain \widetilde A of \Omega, depending only on \Omega and A, and a complex…

Let G be a connected, real, semisimple Lie group contained in its complexification G_C, and let K be a maximal compact subgroup of G. We construct a K_C-G double coset domain in G_C, and we show that the action of G on the K-finite vectors…

In this paper, we first show that a union of upper-level sets associated to fibrewise Lelong numbers of plurisubharmonic functions is in general a pluripolar subset. Then we obtain analyticity theorems for a union of sub-level sets…

Existence of oblique polar lines for the meromorphic extension of the current valued function $\int |f|^{2\lambda}|g|^{2\mu}\square$ is given under the following hypotheses: $f$ and $g$ are holomorphic function germs in $\CC^{n+1}$ such…

A space $G(M, \varPhi)$ of infinitely differentiable functions in ${\mathbb R}^n$ constructed with a help of a family $\varPhi=\{\varphi_m\}_{m=1}^{\infty}$ of real-valued functions $\varphi_m \in~C({\mathbb R}^n)$ and a logarithmically…

A meromorphic function on a compact complex analytic manifold defines a $\bc\infty$ locally trivial fibration over the complement of a finite set in the projective line $\bc\bp^1$. We describe zeta-functions of local monodromies of this…

A relatively polynomially convex subset $V$ of a domain $\Omega$ has the extension property if for every polynomial $p$ there is a bounded holomorphic function $\phi$ on $\Omega$ that agrees with $p$ on $V$ and whose $H^\infty$ norm on…

We extend certain classical theorems in pluripotential theory to a class of functions defined on the support of a $(1,1)$-closed positive current $T$, analogous to plurisubharmonic functions, called $T$-plurisubharmonic functions. These…

We prove that the Szeg\H{o} function, $D(z)$, of a measure on the unit circle is entire meromorphic if and only if the Verblunsky coefficients have an asymptotic expansion in exponentials. We relate the positions of the poles of $D(z)^{-1}$…

We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…

We prove an analogue of E. Levi's Continuity Principle for meromorphic mappings with values in arbitrary compact complex manifolds in place of the Riemann sphere $\cc\pp^1$. The result is achieved by introducing a new extension method for…

It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the whole complex plane. But, in the case of general ($C^{\infty}$) smooth functions, the meromorphic…

In a seminal paper, Choquet introduced an integral formula to extend a monotone increasing setfunction on a sigma-algebra to a (nonlinear) functional on bounded measurable functions. The most important special case is when the setfunction…

We show that any dynamics on any discrete planar sequence $S$ can be realized by the postsingular dynamics of some transcendental meromorphic function, provided we allow for small perturbations of $S$. This work was influenced by an…

If $V$ is an analytic set in a pseudoconvex domain $\Omega$, we show there is always a pseudoconvex domain $G \subseteq \Omega$ that contains $V$ and has the property that every bounded holomorphic function on $V$ extends to a bounded…

In this paper, we consider the non-singular extension problem for circle-valued Morse functions on closed orientable surfaces. The problem asks, given a circle-valued Morse function $f\colon M\to S^{1}$ on a closed orientable surface $M$,…