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Existence of Continuous Functions with a Given Order of Decrease of Least Deviations from Rational Approximations

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Abstract

For a given strictly decreasing sequence {a n } ∞ n=0 of real numbers convergent to zero, we construct a continuous function g on the closed interval [−1,1] such that R 2n(g) and a n have identical order of decrease as n → ∞. Here R n (g) are the best approximations on the closed interval [−1,1] in the uniform norm of the function g by algebraic rational functions of degree at most n.

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  1. Belorussian State University, Belarus

    A. P. Starovoitov

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  1. A. P. Starovoitov
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Starovoitov, A.P. Existence of Continuous Functions with a Given Order of Decrease of Least Deviations from Rational Approximations. Mathematical Notes 74, 701–707 (2003). https://doi.org/10.1023/B:MATN.0000009003.91762.ff

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  • DOI: https://doi.org/10.1023/B:MATN.0000009003.91762.ff

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