On a new approach to the problem of the zero distribution of Hermite-Padé polynomials for a Nikishin system

Abstract

A new approach to the problem of the zero distribution of Hermite-Padé polynomials of type I for a pair of functions $f_1,f_2$ forming a Nikishin system is discussed. Unlike the traditional vector approach, we give an answer in terms of a scalar equilibrium problem with harmonic external field, which is posed on a two-sheeted Riemann surface.

Bibliography: 50 titles

References in corpus (5)

• Sets of Minimal Capacity and Extremal Domains
• Riemann-Hilbert analysis for a Nikishin system
• Some numerical results on the behavior of zeros of the Hermite-Padé polynomials
• On the limit zero distribution of type I Hermite-Padé polynomials
• Zero Distribution of Hermite-Padé Polynomials and Convergence Properties of Hermite Approximants for Multivalued Analytic Functions