On the Łojasiewicz exponent for analytic curves

Jacek Chądzyński; Tadeusz Krasiński

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Resultant and the Łojasiewicz exponent

J. Chądzyński, T. Krasiński (1995)

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An effective formula for the Łojasiewicz exponent of a polynomial mapping of ℂ² into ℂ² at an isolated zero in terms of the resultant of its components is given.

On the order of holomorphic and $c$ -holomorphic functions.

Denkowski, Maciej P. (2007)

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On branches at infinity of a pencil of polynomials in two complex variables

T. Krasiński (1991)

Annales Polonici Mathematici

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Let F ∈ ℂ[x,y]. Some theorems on the dependence of branches at infinity of the pencil of polynomials f(x,y) - λ, λ ∈ ℂ, on the parameter λ are given.

Singular sets of separately analytic functions

Zbigniew Błocki (1992)

Annales Polonici Mathematici

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We complete the characterization of singular sets of separately analytic functions. In the case of functions of two variables this was earlier done by J. Saint Raymond and J. Siciak.

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Frasin, B.A. (2006)

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The analytic fixed point function. II.

Mejía, Diego, Pommerenke, Christian (2006)

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Family of analytic functions of complex order.

Frasin, B.A. (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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New examples of effective formulas for holomorphically contractible functions

Marek Jarnicki, Peter Pflug (1999)

Studia Mathematica

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Let $G \subset ℂ^{n}$ and $B \subset ℂ^{m}$ be domains and let Φ:G → B be a surjective holomorphic mapping. We characterize some cases in which invariant functions and pseudometrics on G can be effectively expressed in terms of the corresponding functions and pseudometrics on B.

The growth of regular functions on algebraic sets

A. Strzeboński (1991)

Annales Polonici Mathematici

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We are concerned with the set of all growth exponents of regular functions on an algebraic subset V of $ℂ^{n}$ . We show that its elements form an increasing sequence of rational numbers and we study the dependence of its structure on the geometric properties of V.

Integral means of certain analytic functions.

Sekine, Tadayuki, Owa, Shigeyoshi, Yamakawa, Rikuo (2005)

General Mathematics

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Diagonal series of rational functions

Sławomir Cynk, Piotr Tworzewski (1991)

Annales Polonici Mathematici

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Some representations of Nash functions on continua in ℂ as integrals of rational functions of two complex variables are presented. As a simple consequence we get close relations between Nash functions and diagonal series of rational functions.

Attenuating the singularities of plurisubharmonic functions

Christer O. Kiselman (1994)

Annales Polonici Mathematici

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We study the singularities of plurisubharmonic functions using methods from convexity theory. Analyticity theorems for a refined Lelong number are proved.