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Sbornik: Mathematics, 2010, Volume 201, Issue 11, Pages 1579–1598
DOI: https://doi.org/10.1070/SM2010v201n11ABEH004123 (Mi sm7691) 		 
This article is cited in 31 scientific papers (total in 31 papers)

Chebyshev representation for rational functions

A. B. Bogatyrevab

a Moscow Institute of Physics and Technology
b Institute of Numerical Mathematics, Russian Academy of Sciences
English version PDF (425 kB) Citations (31)
References:
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DOI: https://doi.org/10.1070/SM2010v201n11ABEH004123
Abstract: An effective representation is obtained for rational functions all of whose critical points, apart from $g-1$, are simple and their corresponding critical values lie in a four-element set. Such functions are described using hyperelliptic curves of genus $g\geqslant1$. The classical Zolotarëv fraction arises in this framework for $g=1$.
Bibliography: 8 titles.
Keywords: rational approximation, Zolotarëv fraction, Riemann surfaces, Abelian integrals.
Received: 11.02.2010 and 19.05.2010
Russian version:
Matematicheskii Sbornik, 2010, Volume 201, Number 11, Pages 19–40
DOI: https://doi.org/10.4213/sm7691
Bibliographic databases:
Document Type: Article
UDC: 517.545
MSC: Primary 41A20; Secondary 30C15, 30F30, 65D20
Language: English
Original paper language: Russian
Citation: A. B. Bogatyrev, “Chebyshev representation for rational functions”, Mat. Sb., 201:11 (2010), 19–40; Sb. Math., 201:11 (2010), 1579–1598
Citation in format AMSBIB
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    • This publication is cited in the following 31 articles:
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    Abstract page:822
    Russian version PDF:336
    English version PDF:21
    References:75
    First page:35
     
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