-pseudoconvex and -complete domains
Giuseppe Vigna Suria (1984)
Compositio Mathematica
Nguyen Quang Dieu (2006)
Publicacions Matemàtiques
We generalize classical results for plurisubharmonic functions and hyperconvex domain to q-plurisubharmonic functions and q-hyperconvex domains. We show, among other things, that Bq-regular domains are q-hyperconvex. Moreover, some smoothing results for q-plurisubharmonic functions are also given.
Per Åhag, Rafał Czyż, Leif Persson (2012)
Annales Polonici Mathematici
In this note we consider radially symmetric plurisubharmonic functions and the complex Monge-Ampère operator. We prove among other things a complete characterization of unitary invariant measures for which there exists a solution of the complex Monge-Ampère equation in the set of radially symmetric plurisubharmonic functions. Furthermore, we prove in contrast to the general case that the complex Monge-Ampère operator is continuous on the set of radially symmetric plurisubharmonic functions. Finally...
P. Heinzner, F. Loose (1994)
Geometric and functional analysis
John Eric Fornaess (1982)
Mathematische Annalen
A. B. Sekerin (1996)
Collectanea Mathematica
The necessary and sufficient condition that a given plurisubharmonic or a subharmonic function admits the representation by the logarithmic potential (up to pluriharmonic or a harmonic term) is obtained in terms of the Radon transform. This representation is applied to the problem of representation of analytic functions by products of primary factors.
Ngaiming Mok (1984)
Mathematische Annalen
T. Bloom, N. Levenberg, S. Ma'u (2003)
Annales Polonici Mathematici
Given a compact set , for each positive integer n, let = := sup: p holomorphic polynomial, 1 ≤ deg p ≤ n. These “extremal-like” functions are essentially one-variable in nature and always increase to the “true” several-variable (Siciak) extremal function, := max[0, sup1/(deg p) log|p(z)|: p holomorphic polynomial, ]. Our main result is that if K is regular, then all of the functions are continuous; and their associated Robin functions increase to for all z outside a pluripolar set....
Jean-Pierre Demailly, János Kollár (2001)
Annales scientifiques de l'École Normale Supérieure
Victor Anandam (2015)
Annales Polonici Mathematici
Let X×Y be the Cartesian product of two locally finite, connected networks that need not have reversible conductance. If X,Y represent random walks, it is known that if X×Y is recurrent, then X,Y are both recurrent. This fact is proved here by non-probabilistic methods, by using the properties of separately superharmonic functions. For this class of functions on the product network X×Y, the Dirichlet solution, balayage, minimum principle etc. are obtained. A unique integral representation is given...
Ulf Backlund, Leif Persson (1998)
Mathematica Scandinavica
Mirosław Baran (1988)
Annales Polonici Mathematici
Józef Siciak (1990)
Colloquium Mathematicae
Urban Cegrell (1985)
Annales Polonici Mathematici
J.E. Fornaess, K. Diederich (1982)
Manuscripta mathematica
Eric Bedford, B.A. Taylor (1988)
Mathematische Zeitschrift
Patrick A.N. Smith (1985/1986)
Mathematische Annalen
Leokadia Białas-Cież (2011)
Banach Center Publications
Let E be a compact set in the complex plane, be the Green function of the unbounded component of with pole at infinity and where the supremum is taken over all polynomials of degree at most n, and . The paper deals with recent results concerning a connection between the smoothness of (existence, continuity, Hölder or Lipschitz continuity) and the growth of the sequence . Some additional conditions are given for special classes of sets.
Laszló Lempert (1983)
Mathematische Annalen
Alessandro Perotti (2000)
Publicacions Matemàtiques
In this paper we investigate some applications of the trace condition for pluriharmonic functions on a smooth, bounded domain in Cn. This condition, related to the normal component on ∂D of the ∂-operator, permits us to study the Neumann problem for pluriharmonic functions and the ∂-problem for (0,1)-forms on D with solutions having assigned real part on the boundary.