Scaled Global Operators and Fueter Variables on Non-zero Scaled Hypercomplex Numbers

Authors

Daniel Alpay, Chapman UniversityFollow
Ilwoo Choo, St. Ambrose UniversityFollow
Mihaela Vajiac, Chapman UniversityFollow

Document Type

Article

Publication Date

10-15-2024

Abstract

In this paper we describe the rise of global operators in the scaled quaternionic case, an important extension from the quaternionic case to the family of scaled hypercomplex numbers H_t, t ∈ R^∗ , of which the H₋₁ = H is the space of quaternions and H₁ is the space of split quaternions.We also describe the scaled Fueter-type variables associated to these operators, developing a coherent theory in this field. We use these types of variables to build different types of function spaces on H_t. Counterparts of the Hardy space and of the Arveson space are also introduced and studied in the present setting. The two different adjoints in the scaled hypercomplex numbers lead to two parallel cases in each instance. Finally we introduce and study the notion of rational function.

Comments

This article was originally published in Advances in Applied Clifford Algebras , volume 34, in 2024. https://doi.org/10.1007/s00006-024-01347-6

Recommended Citation

Alpay, D., Cho, I. & Vajiac, M. Scaled Global Operators and Fueter Variables on Non-zero Scaled Hypercomplex Numbers. Adv. Appl. Clifford Algebras 34, 53 (2024). https://doi.org/10.1007/s00006-024-01347-6

Peer Reviewed

1

Copyright

The authors

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.