On some categories and functors in the theory of quaternionic Bergman spaces
In \(n\)-dimensional spaces \((n\geq 3)\) the class of holomorphic functions is decribed by so called Möbius transformations. The authors work in the algebra of real quaternions and formulate among other statements some kind of a chain rule with a Möbius transformation between conformally equivalent domains. Then hyperholomorphic Bergman spaces are studied in conformally equivalent domains. The authors use the language of categories and functors. In my opinion it is the only paper where this was done up to now. In such a way the generalized Fueter operator induces a functor between corresponding categories of \(\psi\)-hyperholomorphic Bergman spaces.
scientific article; zbMATH DE number 5593795