Abstract
Let f ∈ L 1w [−1, 1], let r n,m(f) be the best rational L 1w -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.
References
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 2, pp. 283–287, February, 2006.
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Blatt, HP., Grothmann, R. & Kovacheva, R.K. Sign changes in rational L 1w -approximation. Ukr Math J 58, 318–323 (2006). https://doi.org/10.1007/s11253-006-0068-7
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DOI: https://doi.org/10.1007/s11253-006-0068-7