Internal characteristics of domains in ℂⁿ

• Autorzy: Vyacheslav Zakharyuta
• Języki publikacji: EN

Abstrakty

EN

This paper is devoted to internal capacity characteristics of a domain D ⊂ ℂⁿ, relative to a point a ∈ D, which have their origin in the notion of the conformal radius of a simply connected plane domain relative to a point. Our main goal is to study the internal Chebyshev constants and transfinite diameters for a domain D ⊂ ℂⁿ and its boundary ∂D relative to a point a ∈ D in the spirit of the author's article [Math. USSR-Sb. 25 (1975), 350-364], where similar characteristics have been investigated for compact sets in ℂⁿ. The central notion of directional Chebyshev constants is based on the asymptotic behavior of extremal monic "polynomials" and "copolynomials" in directions determined by the arithmetic of the index set ℤⁿ. Some results are closely related to results on the sth Reiffen pseudometrics and internal directional analytic capacities of higher order (Jarnicki-Pflug, Nivoche) describing the asymptotic behavior of extremal "copolynomials" in varied directions when approaching the point a.

Kategorie tematyczne

• 32U20: Capacity theory and generalizations
• 32E30: Holomorphic and polynomial approximation, Runge pairs, interpolation
• 32E35: Global boundary behavior of holomorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2014
• Tom: 111
• Numer: 3
• Strony: 215-236

Daty

wydano

2014

Twórcy

autor

Vyacheslav Zakharyuta

• Sabancı University, 34956 Tuzla/İstanbul, Turkey

Identyfikatory

DOI

10.4064/ap111-3-1