Displaying similar documents to “Convergence of holomorphic chains”

On fixed points of holomorphic type

Ewa Ligocka (2002)

Colloquium Mathematicae

Similarity:

We study a linearization of a real-analytic plane map in the neighborhood of its fixed point of holomorphic type. We prove a generalization of the classical Koenig theorem. To do that, we use the well known results concerning the local dynamics of holomorphic mappings in ℂ².

The image of a finely holomorphic map is pluripolar

Armen Edigarian, Said El Marzguioui, Jan Wiegerinck (2010)

Annales Polonici Mathematici

Similarity:

We prove that the image of a finely holomorphic map on a fine domain in ℂ is a pluripolar subset of ℂⁿ. We also discuss the relationship between pluripolar hulls and finely holomorphic functions.

Extending holomorphic maps in infinite dimensions

Bui Dac Tac (1991)

Annales Polonici Mathematici

Similarity:

Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results...

A method of holomorphic retractions and pseudoinverse matrices in the theory of continuation of δ-tempered functions

Marek Jarnicki

Similarity:

CONTENTS§1. Introduction.................................................................................................................5§2. Basic properties of δ-tempered holomorphic functions...............................................8§3. Holomorphic continuation and holomorphic retractions.............................................20§4. Continuation from regular neighbourhoods...............................................................32§5. Continuation from δ-regular submanifolds;...

A note on the Nullstellensatz for c-holomorphic functions

Maciej P. Denkowski (2007)

Annales Polonici Mathematici

Similarity:

We begin this article with a graph theorem and a kind of Nullstellensatz for weakly holomorphic functions. This yields a general Nullstellensatz for c-holomorphic functions on locally irreducible sets. In Section 2 some methods of Płoski-Tworzewski permit us to prove an effective Nullstellensatz for c-holomorphic functions in the case of a proper intersection with the degree of the intersection cycle as exponent. We also extend this result to the case of isolated improper intersection,...

A generalization of Radó's theorem

E. M. Chirka (2003)

Annales Polonici Mathematici

Similarity:

If Σ is a compact subset of a domain Ω ⊂ ℂ and the cluster values on ∂Σ of a holomorphic function f in Ω∖Σ, f' ≢ 0, are contained in a compact null-set for the holomorphic Dirichlet class, then f extends holomorphically onto the whole domain Ω.

The Łojasiewicz exponent of c-holomorphic mappings

Maciej P. Denkowski (2005)

Annales Polonici Mathematici

Similarity:

The aim of this paper is to study the Łojasiewicz exponent of c-holomorphic mappings. After introducing an order of flatness for c-holomorphic mappings we give an estimate of the Łojasiewicz exponent in the case of isolated zero, which is a generalization of the one given by Płoski and earlier by Chądzyński for two variables.