Topologies defined by some invariant pseudodistances

Theodore Barth

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Do Duc Thai (1992)

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We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in $ℂ^{n}$ then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.

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Annales Polonici Mathematici

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A survey of properties of invariant pseudodistances and pseudometrics is given with special stress put on completeness and product property.

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Let $X$ be a complex manifold of dimension at least $2$ which has an exhaustion function whose Levi form has at each point at least $2$ strictly positive eigenvalues. We construct proper holomorphic discs in $X$ through any given point and in any given direction.

Some remarks on holomorphic extension in infinite dimensions

Pham Ban (1994)

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In finite-dimensional complex analysis, the extension of holomorphic maps has been investigated by many authors. In recent years some authors have considered this problem in the infinite-dimensional case. The aim of the present note is to study the extension of holomorphic maps with values in some Banach complex manifolds.

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Holomorphic functions with singularities on algebraic sets.

Sičiak, Józef (2001)

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Annales Polonici Mathematici

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Kriegl, Andreas, Losik, Mark, Michor, Peter W. (2003)

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Approximation of holomorphic mappings on infinite dimensional spaces.

Erhan Çaliskan (2004)

Revista Matemática Complutense

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In this article we examine necessary and sufficient conditions for the predual of the space of holomorphic mappings of bounded type, G(U), to have the approximation property and the compact approximation property and we consider when the predual of the space of holomorphic mappings, G(U), has the compact approximation property. We obtain also similar results for the preduals of spaces of m-homogeneous polynomials, Q(E).