Analyticity of a nonlinear operator associated to the conformal representation of a doubly connected domain in schauder spaces

Abstract

We consider a suitably normalized Riemann map gζ of the plane annulus with , to the plane doubly connected domain enclosed by the pair of Jordan curves , and we present a nonlinear singular integral equation approach to prove that the nonlinear operator which takes the pair of functions to the triple of functions is real analytic in Schauder spaces.