Document Type

Article

Publication Date

6-1-2020

Abstract

In this paper we treat realization results for operator-valued functions which are analytic in the complex sense or slice hyperholomorphic over the quaternions. In the complex setting, we prove a realization theorem for an operator-valued function analytic in a neighborhood of the origin with a coisometric state space operator thus generalizing an analogous result in the unitary case. A main difference with previous works is the use of reproducing kernel Krein spaces. We then prove the counterpart of this result in the quaternionic setting. The present work is the first paper which presents a realization theorem with a state space which is a quaternionic Krein space and may open new avenues of research in hypercomplex analysis.

Comments

NOTICE: this is the author’s version of a work that was accepted for publication in Indagationes Mathematicae. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Indagationes Mathematicae, volume 37, issue 4, in 2020. https://doi.org/10.1016/j.indag.2020.05.005

The Creative Commons license below applies only to this version of the article.

Peer Reviewed

1

Copyright

Royal Dutch Mathematical Society (KWG)

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Available for download on Wednesday, June 01, 2022

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