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arXiv · 1406.6830

Generalized quaternionic Schur functions in the ball and half-space and Krein-Langer factorization

Daniel Alpay·Fabrizio Colombo·Irene Sabadini
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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 $\kappa$ 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.

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Daniel Alpay, Fabrizio Colombo, Irene Sabadini. 2014-06-26. Generalized quaternionic Schur functions in the ball and half-space and Krein-Langer factorization. https://arxiv.org/abs/1406.6830

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