Bicomplex hyperfunctions
The authors continue their study of some aspects of analysis of bicomplex numbers. In their recent work [``Singularities of functions of one and several bicomplex variables'', Ark. Mat. 49, No. 2, 277--294 (2011)] they studied the singularities of holomorphic functions of bicomplex variables. Now they use the sheaf of bicomplex-valued holomorphic functions of \(n\) bicomplex variables in order to define and study hyperfunctions as their relative \(3n\)-cohomology classes. It turns out that such hyperfunctions have their supports on the Euclidean space \(\mathbb{R}^{n}\) embedded into the \(n\)-dimensional bicomplex space \(\mathbb{BC}^{n}\), which allows to construct an abstract Dolbeault complex thus providing a fine resolution for the sheaves of bicomplex holomorphic functions.
scientific article; zbMATH DE number 5903857
scientific article