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Subjects
32-XX Several complex variables and analytic spaces
32Uxx Pluripotential theory
32U20 Capacity theory and generalizations

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Weighted Bernstein-Markov property in ℂⁿ

Nguyen Quang Dieu, Pham Hoang Hiep (2012)

Annales Polonici Mathematici

We study the weighted Bernstein-Markov property for subsets in ℂⁿ which might not be bounded. An application concerning approximation of the weighted Green function using Bergman kernels is also given.

Width asymptotics for a pair of Reinhardt domains

A. Aytuna, A. Rashkovskii, V. Zahariuta (2002)

Annales Polonici Mathematici

For complete Reinhardt pairs “compact set - domain” K ⊂ D in ℂⁿ, we prove Zahariuta’s conjecture about the exact asymptotics $l n d_{s} (A_{K}^{D}) - {((n! s) / τ (K, D))}^{1 / n}$ , s → ∞, for the Kolmogorov widths $d_{s} (A_{K}^{D})$ of the compact set in C(K) consisting of all analytic functions in D with moduli not exceeding 1 in D, τ(K,D) being the condenser pluricapacity of K with respect to D.

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