On a~new approach to the problem of distribution of zeros of Hermite--Pad\'e polynomials for a~Nikishin system

S. P. Suetin

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis, mathematical physics, and applications, Tome 301 (2018), pp. 259-275.

Résumé

A new approach to the problem of the zero distribution of type I Hermite–Padé polynomials 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.

Détail

Keywords: Hermite–Padé polynomials, non-Hermitian orthogonal polynomials, distribution of zeros.

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