A special case of de Branges' theorem on the inverse monodromy problem

We give a new proof of a special case of de Branges' theorem on the inverse monodromy problem: when an associated Riemann surface is of Widom type wit h Direct Cauchy Theorem. The proof is based on our previous result (with M. Sodin) on infinite dimensional Jacobi inversion and on Levin's uniqueness theorem for conformal maps onto comb-like domains. Although in this way we can not prove de Branges' Theorem in full generality, our proof is rather c onstructive and may lead to a multi-dimensional generalization. It could al so shed light on the structure of invariant subspaces of Hardy spaces on Ri emann surfaces of infinite genus.