Sign changes in rational L
w
1
-approximation |
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Authors: | H-P Blatt R Grothmann R K Kovacheva |
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Institution: | 1. Catholic University Eichst?tt-Ingolstadt, Eichst?tt, Germany
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Abstract: | Let f ∈ L
w
1
−1, 1], let r
n,m(f) be the best rational L
w
1
-approximation for f with respect to real rational functions of degree at most n in the numerator and of degree at most m in the denominator, let m = m(n), and let lim
n → ∞ (n-m(n)) = ∞. In this case, we show that the counting measures of certain subsets of sign changes of f-r
n,m
(f) converge weakly to the equilibrium measure on −1, 1] as n → ∞. Moreover, we prove estimates for discrepancy between these counting measures and the equilibrium measure.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 2, pp. 283–287, February, 2006. |
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Keywords: | |
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