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- Title
Criteria for the Best Approximation by Simple Partial Fractions on Semi-Axis and Axis.
- Authors
Komarov, M. A.
- Abstract
We study uniform approximation of real-valued functions f, f(∞) = 0, on ℝ+ and ℝ by real-valued simple partial fractions (the logarithmic derivatives of polynomials). We obtain a criterion for the best approximation on ℝ+ and ℝ in terms of the Chebyshev alternance. This criterion is similar to the known criterion on finite segments. For the problem of approximating odd functions on ℝ we construct an alternance criterion with a weakened condition on the poles of fractions. We present a criterion for the best approximation by simple partial fractions on ℝ+ and ℝ in terms of Kolmogorov. We prove analogs of the de la Vallee-Poussin alternation theorem.
- Subjects
MATHEMATICS theorems; MATHEMATICAL analysis; MATHEMATICAL functions; CHEBYSHEV polynomials; PARTIAL fractions
- Publication
Journal of Mathematical Sciences, 2018, Vol 235, Issue 2, p168
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-018-4066-8