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Some gap power series in multidimensional setting

100%

Siciak J.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2011

tom 65

nr 2

We study extensions of classical theorems on gap power series of a complex variable to the multidimensional case.

Wiener's type regularity criteria on the complex plane

100%

Siciak J.

Annales Polonici Mathematici

1997

tom 66

nr 1

203-221

We present a number of Wiener's type necessary and sufficient conditions (in terms of divergence of integrals or series involving a condenser capacity) for a compact set E ⊂ ℂ to be regular with respect to the Dirichlet problem. The same capacity is used to give a simple proof of the following known theorem [2, 6]: If E is a compact subset of ℂ such that $d(t^{-1}E ∩ {|z-a| ≤ 1}) ≥ const > 0$ for 0 < t ≤ 1 and a ∈ E, where d(F) is the logarithmic capacity of F, then the Green function of ℂ \ E with pole at infinity is Hölder continuous.

On the product property for the transfinite diameter

51%

Błocki Z. , Edigarian A. , Siciak J.

Annales Polonici Mathematici

2011

tom 101

nr 3

209-214

We give a pluripotential-theoretic proof of the product property for the transfinite diameter originally shown by Bloom and Calvi. The main tool is the Rumely formula expressing the transfinite diameter in terms of the global extremal function.

Bounded holomorphic functions with multiple sheeted pluripolar hulls

51%

Edigarian A. , Siciak J. , Zwonek W.

Studia Mathematica

2006

tom 175

nr 3

233-247

We describe compact subsets K of ∂𝔻 and ℝ admitting holomorphic functions f with the domains of existence equal to ℂ∖K and such that the pluripolar hulls of their graphs are infinitely sheeted. The paper is motivated by a recent paper of Poletsky and Wiegerinck.

On series of homogeneous polynomials and their partial sums

44%

Siciak J.

Annales Polonici Mathematici

1990

tom 51

nr 1

289-302

Polynomials and multilinear mappings in topological vector-spaces

38%

Bochnak J. , Siciak J.

Studia Mathematica

1971

tom 39

nr 1

59-76

Approximation by transcendental polynomials

38%

Siciak J.

Annales Polonici Mathematici

1985

tom 46

nr 1

299-309

Singular sets of separately analytic functions

38%

Siciak J.

Colloquium Mathematicum

1990

tom 60-61

nr 1

281-290

Extremal plurisubharmonic functions in $C^N$

38%

Siciak J.

Annales Polonici Mathematici

1981

tom 39

nr 1

175-211

Analytic functions in topological vector-spaces

32%

Bochnak J. , Siciak J.

Studia Mathematica

1971

tom 39

nr 1

77-112