Positive and Generalized Positive Real Lemma for Slice Hyperholomorphic Functions

Authors

Daniel Alpay, Chapman UniversityFollow
Fabrizio Colombo, Politecnico di Milano
Izchak Lewkowicz, Ben Gurion University of the Negev
Irene Sabadini, Politecnico di Milano

Document Type

Article

Publication Date

1-30-2019

Abstract

In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part in the half space of quaternions with positive real part, as well as the case of (generalized) Schur functions in the open unit ball.

Comments

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Integral Equations and Operator Theory, volume 91, in 2019 following peer review. The final publication is available at Springer via DOI: 10.1007/s00020-019-2503-9.

Online access to this article has been shared by the author(s) via Springer Nature SharedIt. Please click here to read a free version of this article.

Recommended Citation

Alpay, D., Colombo, F., Lewkowicz, I. et al. Integr. Equ. Oper. Theory (2019) 91: 4. https://doi.org/10.1007/s00020-019-2503-9

Peer Reviewed

1

Copyright

Springer