Unitary rational functions: The scaled quaternion case
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913575605370880 |
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| author | Alpay, Daniel Cho, Ilwoo Vajiac, Mihaela |
| author_facet | Alpay, Daniel Cho, Ilwoo Vajiac, Mihaela |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06625 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitary rational functions: The scaled quaternion case Alpay, Daniel Cho, Ilwoo Vajiac, Mihaela Functional Analysis 30G35, 46E22 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. |
| title | Unitary rational functions: The scaled quaternion case |
| topic | Functional Analysis 30G35, 46E22 |
| url | https://arxiv.org/abs/2411.06625 |