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Displaying similar documents to “The Pluripolar Hull and the Fine Topology”

On fixed points of holomorphic type

Ewa Ligocka (2002)

Colloquium Mathematicae

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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.

Bounded analytic sets in Banach spaces

Volker Aurich (1986)

Annales de l'institut Fourier

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Conditions are given which enable or disable a complex space X to be mapped biholomorphically onto a bounded closed analytic subset of a Banach space. They involve on the one hand the Radon-Nikodym property and on the other hand the completeness of the Caratheodory metric of X .

Plurifine potential theory

Jan Wiegerinck (2012)

Annales Polonici Mathematici

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We give an overview of the recent developments in plurifine pluripotential theory, i.e. the theory of plurifinely plurisubharmonic functions.

Non-natural topologies on spaces of holomorphic functions

Dietmar Vogt (2013)

Annales Polonici Mathematici

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It is shown that every proper Fréchet space with weak*-separable dual admits uncountably many inequivalent Fréchet topologies. This applies, in particular, to spaces of holomorphic functions, solving in the negative a problem of Jarnicki and Pflug. For this case an example with a short self-contained proof is added.

The image of a finely holomorphic map is pluripolar

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

Annales Polonici Mathematici

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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.

A generalization of Radó's theorem

E. M. Chirka (2003)

Annales Polonici Mathematici

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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.

A note on the Nullstellensatz for c-holomorphic functions

Maciej P. Denkowski (2007)

Annales Polonici Mathematici

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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,...