A note on pluripolar extensions of univalent functions.
Holomorphic functions with singularities on algebraic sets.
Approximation by transcendental polynomials
Extremal plurisubharmonic functions in
On series of homogeneous polynomials and their partial sums
Some gap power series in multidimensional setting
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
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 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....
Singular sets of separately analytic functions
Sets in with vanishing global extremal function and polynomial approximation
Let be a non-pluripolar set in . Let be a function holomorphic in a connected open neighborhood of . Let be a sequence of polynomials with such that We show that if where is a set in such that the global extremal function in , then the maximal domain of existence of is one-sheeted, and for every compact set . If, moreover, the sequence is bounded then . If is a closed set in then...
Families of polynomials and determining measures
Some gap power series in multidimensional setting
We study extensions of classical theorems on gap power series of a complex variable to the multidimensional case.
A note on Alexander's theorem.
Polynomials and multilinear mappings in topological vector-spaces
Analytic functions in topological vector-spaces
Bounded holomorphic functions with multiple sheeted pluripolar hulls
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 the product property for the transfinite diameter
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.
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