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 [9]. We treat both the case of functions with κ 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.
Mathematics Subject Classification (2010). 47A48, 30G35, 30D50.
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© 2014 Springer International Publishing Switzerland
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Alpay, D., Colombo, F., Sabadini, I. (2014). Generalized Quaternionic Schur Functions in the Ball and Half-space and Krein–Langer Factorization. In: Bernstein, S., Kähler, U., Sabadini, I., Sommen, F. (eds) Hypercomplex Analysis: New Perspectives and Applications. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-08771-9_2
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DOI: https://doi.org/10.1007/978-3-319-08771-9_2
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-08770-2
Online ISBN: 978-3-319-08771-9
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