Year: 2026
Type: preprint
Abstract: A new concept of algebras with variable structural constants is introduced as a generalization of classical finite-dimensional algebras. A theory of monogenic functions is developed for a family of two-dimensional commutative associative algebras whose structural constants depend on the variables. Generalized Cauchy–Riemann conditions are obtained, and compatibility conditions for the structural functions are established. It is shown that these compatibility conditions are necessary and sufficient for the product of monogenic functions to remain monogenic. A relationship between monogenic functions and linear partial differential equations with variable coefficients is established. In particular, the components of monogenic functions are shown to satisfy certain second-order linear PDEs with variable coefficients, and converse results are proved. Several explicit examples illustrating the construction of such equations and their solutions are presented.
Source: arXiv (Cornell University)
Author: Shpakivskyi, Vitalii
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Science Foundation Ireland
OpenAlex ID: W7211874355