Page 1

Displaying 1 – 6 of 6

Showing per page

On extremal holomorphically contractible families

Marek Jarnicki, Witold Jarnicki, Peter Pflug (2003)

Annales Polonici Mathematici

We prove (Theorem 1.2) that the category of generalized holomorphically contractible families (Definition 1.1) has maximal and minimal objects. Moreover, we present basic properties of these extremal families.

On perturbations of pluriregular sets generated by sequences of polynomial maps

Maciej Klimek (2003)

Annales Polonici Mathematici

It is shown that an infinite sequence of polynomial mappings of several complex variables, with suitable growth restrictions, determines a filled-in Julia set which is pluriregular. Such sets depend continuously and analytically on the generating sequences, in the sense of pluripotential theory and the theory of set-valued analytic functions, respectively.

On Pólya's Theorem in several complex variables

Ozan Günyüz, Vyacheslav Zakharyuta (2015)

Banach Center Publications

Let K be a compact set in ℂ, f a function analytic in ℂ̅∖K vanishing at ∞. Let f ( z ) = k = 0 a k z - k - 1 be its Taylor expansion at ∞, and H s ( f ) = d e t ( a k + l ) k , l = 0 s the sequence of Hankel determinants. The classical Pólya inequality says that l i m s u p s | H s ( f ) | 1 / s ² d ( K ) , where d(K) is the transfinite diameter of K. Goluzin has shown that for some class of compacta this inequality is sharp. We provide here a sharpness result for the multivariate analog of Pólya’s inequality, considered by the second author in Math. USSR Sbornik 25 (1975), 350-364.

On the Bergman distance on model domains in ℂⁿ

Gregor Herbort (2016)

Annales Polonici Mathematici

Let P be a real-valued and weighted homogeneous plurisubharmonic polynomial in n - 1 and let D denote the “model domain” z ∈ ℂⁿ | r(z):= Re z₁ + P(z’) < 0. We prove a lower estimate on the Bergman distance of D if P is assumed to be strongly plurisubharmonic away from the coordinate axes.

On the Green function on a certain class of hyperconvex domains

Gregor Herbort (2008)

Annales Polonici Mathematici

We study the behavior of the pluricomplex Green function on a bounded hyperconvex domain D that admits a smooth plurisubharmonic exhaustion function ψ such that 1/|ψ| is integrable near the boundary of D, and moreover satisfies the estimate | ψ | C e x p ( - C ' ( l o g ( 1 / δ D ) ) α ) at points close enough to the boundary with constants C,C’ > 0 and 0 < α < 1. Furthermore, we obtain a Hopf lemma for such a function ψ. Finally, we prove a lower bound on the Bergman distance on D.

On the multivariate transfinite diameter

Thomas Bloom, Jean-Paul Calvi (1999)

Annales Polonici Mathematici

We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.

Currently displaying 1 – 6 of 6

Page 1