One-sided weighted integral approximation of characteristic functions of intervals by polynomials on a closed interval

A. G. Babenko; M. V. Deikalova; Sz. G. Revesz

doi:10.1134/S0081543817050029

One-sided weighted integral approximation of characteristic functions of intervals by polynomials on a closed interval

Авторы: Babenko A.G.¹^,2, Deikalova M.V.¹^,2, Revesz S.G.³
Учреждения:
1. Krasovskii Institute of Mathematics and Mechanics
2. Ural Federal University
3. Alfréd Rényi Institute of Mathematics
Выпуск: Том 297, № Suppl 1 (2017)
Страницы: 11-18
Раздел: Article
URL: https://journals.rcsi.science/0081-5438/article/view/174720
DOI: https://doi.org/10.1134/S0081543817050029
ID: 174720

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Аннотация

We consider the problem of one-sided weighted integral approximation on the interval [−1, 1] to the characteristic functions of intervals (a, 1] ⊂ (−1, 1] and (a, b) ⊂ (−1, 1) by algebraic polynomials. In the case of half-intervals, the problem is solved completely. We construct an example to illustrate the difficulties arising in the case of an open interval.