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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
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
Citation:
A. B. Bogatyrev, “Chebyshev representation for rational functions”, Sb. Math., 201:11 (2010), 1579–1598
Linking options:
https://www.mathnet.ru/eng/sm7691https://doi.org/10.1070/SM2010v201n11ABEH004123 https://www.mathnet.ru/eng/sm/v201/i11/p19
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Abstract page: | 831 | Russian version PDF: | 337 | English version PDF: | 22 | References: | 76 | First page: | 35 |
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