Geodesic
Distribution of Alternation Points in Best Rational Approximations
Matematičeskie zametki, Tome 83 (2008) no. 4, pp. 493-502

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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, equilibrium measure, counting measure, Chebyshev (Walsh) table, Chebyshev rational operator.
Mots-clés : alternation point 
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     author = {A. I. Bogolyubskii},
     title = {Distribution of {Alternation} {Points} in {Best} {Rational} {Approximations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {493--502},
     publisher = {mathdoc},
     volume = {83},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_4_a1/}
}
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A. I. Bogolyubskii. Distribution of Alternation Points in Best Rational Approximations. Matematičeskie zametki, Tome 83 (2008) no. 4, pp. 493-502. http://geodesic.mathdoc.fr/item/MZM_2008_83_4_a1/