Differentiation and Certain Operators on Scaled Sectional Hypercomplex Numbers

Authors

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

Document Type

Article

Publication Date

8-6-2025

Abstract

In this paper, we study certain sectional structures of the t-scaled hypercomplex numbers H_t for a scale t ∈ R, including the quaternions H_-1, and the split quaternions H₁. For a fixed scale t ∈ R, by defining the collection S_t of certain pureimaginary t-scaled hypercomplex number in H_t , we sectionize H_t from the imaginaries of S_t. We concentrate on a section SH_It for an arbitrarily fixed imaginary I_t ∈ S_t , called the t-scaled section for I_t. Differentiation theory on the section SH_It is studied in terms of that on H_t by regarding SH_It as a sub-structure of H_t . Also, some functional vector spaces induced by SH_It over the real field R are constructed and analyzed. And then an interesting type of operators on one of our vector spaces is considered. In particular, we are interested in Toeplitz-like operators. The main tool to do them is the isomorphic relation between SH_It and the t-scaled hyperbolics D_t , for “all” I_t ∈ S_t , for any scale t ∈ R.

Comments

This article was originally published in Journal of Analysis in 2025. https://doi.org/10.1007/s41478-025-00951-4

Recommended Citation

Alpay, D., Cho, I. Differentiation and certain operators on scaled sectional hypercomplex numbers. J Anal (2025). https://doi.org/10.1007/s41478-025-00951-4

Peer Reviewed

1

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