Variation of the equilibrium energy and the S-property of stationary compact sets

A. Martínez-Finkelshtein; E. A. Rakhmanov; S. P. Suetin

doi:10.1070/SM2011v202n12ABEH004209

Variation of the equilibrium energy and the S-property of stationary compact sets

A. Martínez-Finkelshtein
, E. A. Rakhmanov
, S. P. Suetin

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

This paper studies a variation of the equilibrium energy for a certain fairly general functional which appears naturally in the solution of many rational approximation problems of multi-valued analytic functions. The main result of this work states that for the energy functional under consideration and a certain class of admissible compact sets, related to the function to be approximated, the corresponding stationary compact set is fully characterized by the so-called S-property.

Original language	English
Pages (from-to)	1831-1852
Number of pages	22
Journal	Sbornik Mathematics
Volume	202
Issue number	12
DOIs	https://doi.org/10.1070/SM2011v202n12ABEH004209
State	Published - 1 Dec 2011
Externally published	Yes

Keywords

Equilibrium distributions
Orthogonal polynomials
Padé approximants
Rational approximation
S-property
Stationary compact set

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1070/SM2011v202n12ABEH004209

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abstract = "This paper studies a variation of the equilibrium energy for a certain fairly general functional which appears naturally in the solution of many rational approximation problems of multi-valued analytic functions. The main result of this work states that for the energy functional under consideration and a certain class of admissible compact sets, related to the function to be approximated, the corresponding stationary compact set is fully characterized by the so-called S-property.",

keywords = "Equilibrium distributions, Orthogonal polynomials, Pad{\'e} approximants, Rational approximation, S-property, Stationary compact set",

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AU - Suetin, S. P.

PY - 2011/12/1

Y1 - 2011/12/1

N2 - This paper studies a variation of the equilibrium energy for a certain fairly general functional which appears naturally in the solution of many rational approximation problems of multi-valued analytic functions. The main result of this work states that for the energy functional under consideration and a certain class of admissible compact sets, related to the function to be approximated, the corresponding stationary compact set is fully characterized by the so-called S-property.

AB - This paper studies a variation of the equilibrium energy for a certain fairly general functional which appears naturally in the solution of many rational approximation problems of multi-valued analytic functions. The main result of this work states that for the energy functional under consideration and a certain class of admissible compact sets, related to the function to be approximated, the corresponding stationary compact set is fully characterized by the so-called S-property.

KW - Equilibrium distributions

KW - Orthogonal polynomials

KW - Padé approximants

KW - Rational approximation

KW - S-property

KW - Stationary compact set

UR - https://www.scopus.com/pages/publications/84857397852

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DO - 10.1070/SM2011v202n12ABEH004209

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ER -

Variation of the equilibrium energy and the S-property of stationary compact sets

Abstract

Keywords

ASJC Scopus subject areas

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