Analytic continuation and decomposition of conformal mappings into partial fractions (Q5942131)

The authors consider a problem of analytic continuation of analytic functions beyond ellipse type arcs, provided that either the real part or the modulus of the function in question is constant. They study the cases of a half plane and a disk. The results are applied to obtain partial fraction decompositions for conformal mappings which map domains with elliptical boundaries onto a disk or a half plane. In the case of an ellipse they prove that the conformal mappings are meromorphic functions with a countable number of second order or simple poles.