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Computing Walsh's conformal map onto lemniscatic domains

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The conformal mapping of multiply connected domains onto lemniscatic domains was introduced by Walsh in 1956. Walsh's map is a direct generalization of the Riemann mapping. Several important quantities, such as the Green's function with pole at infinity of the multiply connected domain, or the logarithmic capacity of its complemet, can be read of the lemniscatic domain and Walsh's map. In this talk, we discuss the computation of this conformal mapping and lemniscatic domain. This is based on joint work with Jörg Liesen and Mohamed Nasser.

This talk is part of the Isaac Newton Institute Seminar Series series.

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