This article is cited in 29 papers

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

A. Martínez-Finkelshtein^a, E. A. Rakhmanov^bc, S. P. Suetin<sup>b

a</sup> University of Almeria, Spain
^b Steklov Mathematical Institute, Russian Academy of Sciences
^c University of South Florida, USA

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.
Bibliography: 38 titles.

Keywords: rational approximation, orthogonal polynomials, Padé approximants, equilibrium distributions, stationary compact set, $S$-property.

UDC: 517.53

MSC: 31A15

Received: 14.02.2011 and 29.09.2011

DOI: 10.4213/sm7854

 English version: Sbornik: Mathematics, 2011, 202:12, 1831–1852

Bibliographic databases:

• 
• 
• 
• 
• 
•