Abstract
Letf ∈L p (I) and denote byB n,p (f) the polynomial of bestL p-approximation tof of degreen (1<p<∞,I=[−1,1], the norm is weightedL p-norm with an arbitrary positive weight). Extending a result proved by Saff and Shekhtman forp=2 we show that for every 1<p<∞ andf ∈L p (I) (not a polynomial) points of sign change of the error functionf-B n,p (f) are dense inI asn→∞.
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Communicated by Vilmos Totik.
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Kroó, A., Swetits, J.J. On density of interpolation points, a Kadec-type theorem, and Saff's principle of contamination inL p-approximation. Constr. Approx 8, 87–103 (1992). https://doi.org/10.1007/BF01208908
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DOI: https://doi.org/10.1007/BF01208908