On Sign Changes in Weighted Polynomial l^1-Approximation

Authors: Blatt H.-P.1; Grothmann, R.2; Kovacheva, R.K.3

Source: Acta Mathematica Hungarica, Volume 95, Number 4, May 2002 , pp. 309-322(14)

Publisher: Springer

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Abstract:

For f \in L_w^1 [-1, 1] denote by B_{n, 1} (f), n = 0, 1, \dots a polynomial of best weighted L^1-approximation to f on [-1, 1] of degree \le n. In the present paper, we are dealing with the asymptotic distribution of sign changes of the error functions f - B_{n, 1} (f).

Keywords: best weighted approximation; counting measure; sign changes

Document Type: Regular Paper

Affiliations: 1: KATHOLISCHE UNIVERSITÄT EICHSTÄTT MATHEMATISCH-GEOGRAPHISCHE FAKULTÄT D-85071 EICHSTÄTT E-mail: HANS.BLATT@KU-EICHSTAETT.DE 2: KATHOLISCHE UNIVERSITÄT EICHSTÄTT MATHEMATISCH-GEOGRAPHISCHE FAKULTÄT D-85071 EICHSTÄTT E-mail: GROTHM@KU-EICHSTAETT.DE 3: KATHOLISCHE UNIVERSITÄT EICHSTÄTT MATHEMATISCH-GEOGRAPHISCHE FAKULTÄT D-85071 EICHSTÄTT

Publication date: May 1, 2002

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