Factorizations of analytic self-maps of the upper half-plane

Abstract

We extend a factorization due to Kreuon to arbitrary analytic func- tions from the upper half-plane to itself. The factorization represents every such function as a product of fractional linear factors times a function which, generally, has fewer zeros and singularities than the original one. The reult is used to construct functions with given zeros and poles on the real line.