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Matematicheskie Zametki, 2008, Volume 83, Issue 4, Pages 493–502
DOI: https://doi.org/10.4213/mzm4570 (Mi mzm4570) 		 
Distribution of Alternation Points in Best Rational Approximations

A. I. Bogolyubskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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DOI: https://doi.org/10.4213/mzm4570
Abstract: We study the convergence of counting measures of alternation point sets in best rational approximations to the equilibrium measure. It is shown that, for any prescribed nondecreasing sequence of denominator degrees, there exists a function analytic on $[0,1]$ and a sequence of numerator degrees such that the corresponding sequence of measures does not converge to the equilibrium measure of the interval.
Keywords: best rational approximation, alternation point, equilibrium measure, counting measure, Chebyshev (Walsh) table, Chebyshev rational operator.
Received: 02.05.2007
Revised: 15.10.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 4, Pages 454–462
DOI: https://doi.org/10.1134/S0001434608030188
Bibliographic databases:
UDC: 517.518.8
Language: Russian
Citation: A. I. Bogolyubskii, “Distribution of Alternation Points in Best Rational Approximations”, Mat. Zametki, 83:4 (2008), 493–502; Math. Notes, 83:4 (2008), 454–462
Citation in format AMSBIB
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