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Sbornik: Mathematics, 2020, Volume 211, Issue 10, Pages 1486–1502
DOI: https://doi.org/10.1070/SM8634 (Mi sm8634) 		 
This article is cited in 16 scientific papers (total in 16 papers)

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
English version PDF (490 kB) Citations (16)
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DOI: https://doi.org/10.1070/SM8634
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-а
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 14-01-00604-a).
Received: 16.11.2015 and 30.05.2020
Russian version:
Matematicheskii Sbornik, 2020, Volume 211, Number 10, Pages 139–156
DOI: https://doi.org/10.4213/sm8634
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: 41A21, 42C05
Language: English
Original paper language: Russian
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
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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