Effective Discretization of the Energy Integral and Grunsky Coefficients in Annuli |
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Authors: | Marcus Stiemer |
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Institution: | (1) Universitat Dortmund, Fachbereich Mathematik, 44221 Dortmund, Germany |
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Abstract: | Let be an analytic Jordan curve in the complex plane.
We formulate a discrete minimal energy problem in a suitable class of functions
whose solution provides a geometrically fast converging approximation to the
equilibrium measure of . For this purpose an extremal point system that was introduced by K. Menke in 1972
is applied. In particular, an explicit error bound for the
discretization of the energy integral is computed.
The key to this error estimate is a univalence criterion for Laurent series,
proved by R. Kuhnau in 1972.
Finally, an estimate for the discrepancy between the
approximating measures and the equilibrium measure is derived from the
discretization error of the energy integral. |
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Keywords: | Energy integral Equilibrium Grunsky coefficients |
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