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On Sign Changes in Weighted Polynomial L^1 -Approximation

Authors:	H-P Blatt R Grothmann R K Kovacheva

Institution:	(1) KATHOLISCHE UNIVERSITÄT EICHSTÄTT MATHEMATISCH-GEOGRAPHISCHE FAKULTÄT, D-85071 EICHSTÄTT E-mail

Abstract:	For $f \in L_{^w }^1 \left { - 1{\text{,}}1} \right]$ denote by $B_{n,1} \left( f \right),n = 0,1,...a$ a polynomial of best weighted -approximation to on $\left { - 1{\text{,}}1} \right]$ of degree $\leqq n$ . In the present paper, we are dealing with the asymptotic distribution of sign changes of the error functions $f - B_{n,1} \left( f \right)$ .

Keywords:	sign changes best weighted approximation counting measure
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