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

Babenko, A. G. and Deikalova, Marina V. and Révész, Szilárd (2017) One-sided weighted integral approximation of characteristic functions of intervals by polynomials on a closed interval. Proceedings of the Steklov Institute of Mathematics, 297. pp. 11-18. ISSN 0081-5438

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Abstract

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. © 2017, Pleiades Publishing, Ltd.

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