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Displaying 141 – 160 of 346

Holomorphic approximation in infinite-dimensional Riemann domains

Jorge Mujica (1985)

Studia Mathematica

Holomorphic convexity of spaces of analytic cycles

François Norguet, Yum-Tong Siu (1977)

Bulletin de la Société Mathématique de France

Holomorphic functions of fast growth on submanifolds of the domain

Piotr Jakóbczak (1998)

Annales Polonici Mathematici

We construct a function f holomorphic in a balanced domain D in $ℂ^{N}$ such that for every positive-dimensional subspace Π of $ℂ^{N}$ , and for every p with 1 ≤ p < ∞, ${f |}_{Π \cap D}$ is not $L^{p}$ -integrable on Π ∩ D.

Holomorphic functions on locally convex topological vector spaces. II. Pseudo convex domains

Sean Dineen (1973)

Annales de l'institut Fourier

In this article we discuss the relationship between domains of existence domains of holomorphy, holomorphically convex domains, pseudo convex domains, in the context of locally convex topological vector spaces. By using the method of Hirschowitz for $Π_{n = 1}^{\infty} C$ and the method used for Banach spaces with a basis we prove generalisations of the Cartan-Thullen-Oka-Norguet-Bremmerman theorem for finitely polynomially convex domains in a variety of locally convex spaces which include the following:1) $N$ -projective...

Holomorphic generators of some ideals in $C^{\infty} (\bar{D})$

Paolo de Bartolomeis (1987)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Holomorphic line bundles on a domain of a two-dimensional Stein manifold

Makoto Abe (2004)

Annales Polonici Mathematici

Let D be an open subset of a two-dimensional Stein manifold S. Then D is Stein if and only if every holomorphic line bundle L on D is the line bundle associated to some (not necessarily effective) Cartier divisor 𝔡 on D.

Holomorphic Lipschitz functions and application to the $v \partial$ -problem

Der-Chen Chang, Steven Krantz (1991)

Colloquium Mathematicae

Holomorphic mapping of annuli in $C^{n}$ and the associated extremal function

Eric Bedford, Dan Burns (1979)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Hyperconvexity of non-smooth pseudoconvex domains

Xu Wang (2014)

Annales Polonici Mathematici

We show that a bounded pseudoconvex domain D ⊂ ℂⁿ is hyperconvex if its boundary ∂D can be written locally as a complex continuous family of log-Lipschitz curves. We also prove that the graph of a holomorphic motion of a bounded regular domain Ω ⊂ ℂ is hyperconvex provided every component of ∂Ω contains at least two points. Furthermore, we show that hyperconvexity is a Hölder-homeomorphic invariant for planar domains.