English

Representation of Quaternionic $\psi$-hyperholomorphic Functions

Complex Variables 2023-11-16 v1 Analysis of PDEs Operator Algebras

Abstract

In the algebra of complex quaternions H(C)\mathbb{H(C)} we consider for the first time left- and right-ψ\psi-hyperholomorphic functions. We justify the transition in left- and right-ψ\psi-hyperholomorphic functions to a simpler basis i.e. to the Cartan basis. Using Cartan's basis we find the solution of Cauchy-Fueter equation. By the same method we find a representation of left-ψ\psi-hyperholomorphic function in a special case.

Keywords

Cite

@article{arxiv.2311.08522,
  title  = {Representation of Quaternionic $\psi$-hyperholomorphic Functions},
  author = {Tetiana Kuzmenko and Vitalii Shpakivskyi},
  journal= {arXiv preprint arXiv:2311.08522},
  year   = {2023}
}
R2 v1 2026-06-28T13:21:21.983Z