, Volume 190, Issue 2, pp 247-261

Bicomplex hyperfunctions

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Abstract

In this paper, we consider bicomplex holomorphic functions of several variables in ${{\mathbb B}{\mathbb C}^n}$ .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 ${{\mathbb R}^n}$ within the bicomplex space ${{\mathbb B}{\mathbb C}^n}$ , 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.