Internal characteristics of domains in ℂⁿ

Vyacheslav Zakharyuta. "Internal characteristics of domains in ℂⁿ." Annales Polonici Mathematici 111.3 (2014): 215-236. <http://eudml.org/doc/281120>.

@article{VyacheslavZakharyuta2014,
abstract = {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.},
author = {Vyacheslav Zakharyuta},
journal = {Annales Polonici Mathematici},
keywords = {transfinite diameter; Chebyshev constants; pluripotential Green functions; capacities},
language = {eng},
number = {3},
pages = {215-236},
title = {Internal characteristics of domains in ℂⁿ},
url = {http://eudml.org/doc/281120},
volume = {111},
year = {2014},
}

TY - JOUR
AU - Vyacheslav Zakharyuta
TI - Internal characteristics of domains in ℂⁿ
JO - Annales Polonici Mathematici
PY - 2014
VL - 111
IS - 3
SP - 215
EP - 236
AB - 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.
LA - eng
KW - transfinite diameter; Chebyshev constants; pluripotential Green functions; capacities
UR - http://eudml.org/doc/281120
ER -