Local discrepancy theorems for the distributions of zeros of polynomials (Q2781655)

Blatt and Mhaskar estimated the discrepancy of a signed Borel measure \(\sigma\) on a sufficiently smooth Jordan curve or arc \(L\) in terms of a two-sided bound for the logarithmic potential of \(\sigma\) on level curves of Green's function \(G(z)\) of \(\bar{\mathbb C}\setminus L\). In this paper we obtain local estimates for the discrepancy of \(\sigma\) on subarcs of \(L\) by using local two-sided bounds for the logarithmic potential. The theorem leads to local estimates for the zeros of Jacobi polynomials which are better than so far known global estimates (authors' abstract).NEWLINENEWLINEFor the entire collection see [Zbl 0971.00015].