Abstract.
In [7], Blatt and Mhaskar estimated the Erdős-Turán type discrepancy of a signed Borel measure σ on a sufficiently smooth Jordan curve or arc L in terms of the logarithmic potential of σ on a curve enclosing L. We extend this result to a measure σ on an arbitrary quasiconformal curve. As applications, estimates for the distribution of simple zeros of monic polynomials, Fekete points, extreme points of polynomials of best uniform approximation are obtained.
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Date received: August 9, 1995. Date revised: December 21, 1995.
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Andrievskii, V., Blatt, HP. A Discrepancy Theorem on Quasiconformal Curves. Constr. Approx. 13, 363–379 (1997). https://doi.org/10.1007/s003659900048
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DOI: https://doi.org/10.1007/s003659900048