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 Mat. Sb., 2020, Volume 211, Number 10, Pages 139–156 (Mi msb8634)

Hermite-Padé approximants to the Weyl function and its derivative for discrete measures

V. N. Sorokin

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: Hermite-Padé approximants of the second kind to the Weyl function and its derivatives are investigated. The Weyl function is constructed from the orthogonal Meixner polynomials. The limiting distribution of the zeros of the common denominators of these approximants, which are multiple orthogonal polynomials for a discrete measure, is found. It is proved that the limit measure is the unique solution of the equilibrium problem in the theory of the logarithmic potential with an Angelesco matrix. The effect of pushing some zeros off the real axis to some curve in the complex plane is discovered. An explicit form of the limit measure in terms of algebraic functions is given.
Bibliography: 10 titles.

Keywords: Meixner polynomials, equilibrium problems in logarithmic potential theory, Riemann surfaces, algebraic functions.

 Funding Agency Grant Number Russian Foundation for Basic Research 14-01-00604-à This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 14-01-00604-a).

DOI: https://doi.org/10.4213/sm8634

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English version:
Sbornik: Mathematics, 2020, 211:10, 1486–1502

UDC: 517.53
MSC: 41A21, 42C05

Citation: V. N. Sorokin, “Hermite-Padé approximants to the Weyl function and its derivative for discrete measures”, Mat. Sb., 211:10 (2020), 139–156; Sb. Math., 211:10 (2020), 1486–1502

Citation in format AMSBIB
\Bibitem{Sor20} \by V.~N.~Sorokin \paper Hermite-Pad\'e approximants to the Weyl function and its derivative for discrete measures \jour Mat. Sb. \yr 2020 \vol 211 \issue 10 \pages 139--156 \mathnet{http://mi.mathnet.ru/msb8634} \crossref{https://doi.org/10.4213/sm8634} \transl \jour Sb. Math. \yr 2020 \vol 211 \issue 10 \pages 1486--1502 \crossref{https://doi.org/10.1070/SM8634}