In this paper, we consider bicomplex holomorphic functions of several variables in BCn .We use the sheaf of these functions to define and study hyperfunctions as their relative 3n-cohomology classes. We show that such hyperfunctions are supported by the Euclidean space Rn within the bicomplex space BCn , and we construct an abstract Dolbeault complex that provides a fine resolution for the sheaves of bicomplex holomorphic functions. As a corollary, we show how that the bicomplex hyperfunctions can be represented as classes of differential forms of degree 3n − 1.
Colombo, F., Sabadini, I., Struppa, D. C., Vajiac, A., & Vajiac, M. (2011). Bicomplex hyperfunctions. Annali di Matematica Pura ed Applicata, 190(2), 247-261. doi: 10.1007/s10231-010-0148-z
This article was originally published in Annali di Matematica Pura ed Applicata, volume 190, issue 2, in 2011. DOI: 10.1007/s10231-010-0148-z