Abstract
Letw be a suitable weight function,B n,p denote the polynomial of best approximation to a functionf inL p w [−1, 1],v n be the measure that associates a mass of 1/(n+1) with each of then+1 zeros ofB n+1,p−B n,p and μ be the arcsine measure defined by\(d\mu : = (\pi \sqrt {1 - x^2 } )^{ - 1} dx\). We estimate the rate at which the sequencev n converges to μ in the weak-* topology. In particular, our theorem applies to the zeros of monic polynomials of minimalL pw norm.
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This author gratefully acknowledges partial support from NSA contract #A4235802 during 1992, AFSOR Grant 226113 during 1993 and The Alexander von Humboldt Foundation during both of these years.
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Blatt, H.P., Mhaskar, H.N. A discrepancy theorem concerning polynomials of best approximation inL p w [−1, 1]. Monatshefte für Mathematik 120, 91–103 (1995). https://doi.org/10.1007/BF01585910
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DOI: https://doi.org/10.1007/BF01585910