Abstract
From the numerous systems of points and associated monic polynomials to which discrepancy theorems can be applied we choose Fekete points for compact sets E of ℂ. It is known that the counting measures for Fekete point sets converge to the equilibrium distribution of E. Furthermore, if E is a Jordan curve or arc, then this weak*-convergence can be estimated by discrepancy bounds. For analytic Jordan curves Pommerenke [144, 145] has proved sharp asymptotic estimates, which can be found in Section 7.2.
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Andrievskii, V.V., Blatt, HP. (2002). Applications of Discrepancy Theorems. In: Discrepancy of Signed Measures and Polynomial Approximation. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4999-1_7
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DOI: https://doi.org/10.1007/978-1-4757-4999-1_7
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