Generalized quaternionic Schur functions in the ball and half-space and Krein-Langer factorization
Abstract
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 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.
Cite
@article{arxiv.1406.6830,
title = {Generalized quaternionic Schur functions in the ball and half-space and Krein-Langer factorization},
author = {Daniel Alpay and Fabrizio Colombo and Irene Sabadini},
journal= {arXiv preprint arXiv:1406.6830},
year = {2014}
}
Comments
to appear in Hypercomplex Analysis: New perspectives and applications, S. Bernstein et al. eds., Trends in Mathematics Birkh\"auser, Basel, 2014