A discrepancy theorem concerning polynomials of best approximation inL w p [−1, 1

Abstract

Letw be a suitable weight function,Bn,p denote the polynomial of best approximation to a functionf inLwp[−1, 1],vn be the measure that associates a mass of 1/(n+1) with each of then+1 zeros ofBn+1,p−Bn,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 sequencevn converges to μ in the weak-* topology. In particular, our theorem applies to the zeros of monic polynomials of minimalLwp norm.