%0 Journal Article
%T Generalized quaternionic Schur functions in the ball and half-space and Krein-Langer factorization
%A Daniel Alpay
%A Fabrizio Colombo
%A Irene Sabadini
%J Mathematics
%D 2014
%I arXiv
%X In this paper we prove a new version of Krein-Langer factorization theorem in the slice hyperholomorphic setting which is more general than the one proved in [D. Alpay, F. Colombo, I. Sabadini, Krein-Langer factorization and related topics in the slice hyperholomorphic setting, J. Geom. Anal., 24 (2014), 843--872]. We treat both the case of functions with $\kappa$ negative squares defined on subsets of the quaternionic unit ball or on subsets of the half space of quaternions with positive real part. A crucial tool in the proof of our results is the Schauder-Tychonoff theorem and an invariant subspace theorem for contractions in a Pontryagin space.
%U http://arxiv.org/abs/1406.6830v1