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We derive analytic series representation for the Neumann-Poincare operatorusing the exterior conformal mapping for general shape domains. We derive theformula by using the Faber polynomial basis for arbitrary Lipschitz domains.With the proposed method we can approximate the spectrum of the smooth domainsby finding the eigenvalues of matrices. We also find the connection of theboundary integral equations with the exterior conformal mapping, explicitly.

A new series solution method for the transmission problem