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Mat. Zametki, 2003, Volume 74, Issue 5, Pages 745–751 (Mi mz307)  

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

A. P. Starovoitov

Belarusian State University, Faculty of Mathematics and Mechanics

Abstract: For a given strictly decreasing sequence $\{a_n\}^\infty_{n=0}$ 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 $n\to\infty$. 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 $n$.

DOI: https://doi.org/10.4213/mzm307

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English version:
Mathematical Notes, 2003, 74:5, 701–707

Bibliographic databases:

UDC: 517.51+517.53
Received: 15.01.2002
Revised: 17.02.2003

Citation: A. P. Starovoitov, “Existence of Continuous Functions with a Given Order of Decrease of Least Deviations from Rational Approximations”, Mat. Zametki, 74:5 (2003), 745–751; Math. Notes, 74:5 (2003), 701–707

Citation in format AMSBIB
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\pages 701--707
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