Geodesic
Weighted one-sided approximation of characteristic functions of intervals by polynomials on a closed interval
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 46-53

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We consider the problem of weighted one-sided approximation on the interval $[-1,1]$ of characteristic functions of intervals $(a,1]\subset(-1,1]$ and $(a,b)\subset(-1,1)$ by algebraic polynomials. In the case of half-intervals, the problem is solved completely. We construct an example to illustrate difficulties arising in the case of an open interval.
Keywords: one-sided approximation, characteristic function, polynomials. 
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     title = {Weighted one-sided approximation of characteristic functions of intervals by polynomials on a closed interval},
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A. G. Babenko; M. V. Deikalova; S. G. Revesz. Weighted one-sided approximation of characteristic functions of intervals by polynomials on a closed interval. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 46-53. http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a4/