Internal characteristics of domains in C-n

Warning The system is temporarily closed to updates for reporting purpose.

Zakharyuta, Vyacheslav (2014) Internal characteristics of domains in C-n. Annales Polonici Mathematici, 111 (3). pp. 215-236. ISSN 0066-2216 (Print) 1730-6272 (Online)

[thumbnail of This is a RoMEO green journal -- author can archive pre-print (ie pre-refereeing)] PDF (This is a RoMEO green journal -- author can archive pre-print (ie pre-refereeing))
ccd8.pdf

Download (247kB)

Abstract

This paper is devoted to internal capacity characteristics of a domain D subset of C-n, relative to a point a is an element of 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 subset of C-n and its boundary partial derivative D relative to a point a is an element of 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 C-n. 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 Z(n). 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.
Item Type: Article
Uncontrolled Keywords: transfinite diameter; Chebyshev constants; pluripotential Green functions; capacities; Vandermondian; Wronskian
Subjects: Q Science > QA Mathematics > QA299.6-433 Analysis
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Vyacheslav Zakharyuta
Date Deposited: 23 Dec 2014 20:28
Last Modified: 02 Aug 2019 14:31
URI: https://research.sabanciuniv.edu/id/eprint/25469

Actions (login required)

View Item
View Item