Document Type
Article
Publication Date
2-2-2026
Abstract
We develop the theory of minimal realizations and factorizations of rational functions where the coefficient space is a ring of the type introduced in our previous work, the scaled quaternions, which includes as special cases the quaternions and the split quaternions. The methods involved are not a direct generalization of the complex or quaternionic settings, and in particular, the adjoint is not the classical adjoint and we use properties of real Hilbert spaces. This adjoint allows to define the counterpart of unitarity for matrix-rational functions, and we develop the corresponding theories of realizations and unitary factorizations. We also begin a theory of matrices in the underlying rings.
Recommended Citation
Alpay, D., Cho, I. & Vajiac, M. Unitary Rational Functions: The Scaled Quaternion Case. Integr. Equ. Oper. Theory 98, 5 (2026). https://doi.org/10.1007/s00020-025-02822-w
Peer Reviewed
1
Copyright
The authors
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Comments
This article was originally published in Integral Equations and Operator Theory, volume 98, in 2026. https://doi.org/10.1007/s00020-025-02822-w