Abstract
By using Riemann surface theory we obtain results on quadrature domains and identities for analytic functions, e.g., existence of multiply-connected quadrature domains, descriptions of their algebraic boundaries and results on the multitude of quadrature domains associated to a fixed quadrature identity. The main idea is to characterize quadrature domains in terms of meromorphic functions and differentials on Riemann surfaces conformally equivalent to the Schottky doubles of the domains.
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Gustafsson, B. Quadrature identities and the schottky double. Acta Appl Math 1, 209–240 (1983). https://doi.org/10.1007/BF00046600
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DOI: https://doi.org/10.1007/BF00046600