Bicomplex Hyperfunctions

Authors

Fabrizio Colombo, Politecnico di Milano
Irene Sabadini, Politecnico di Milano
Daniele C. Struppa, Chapman UniversityFollow
Adrian Vajiac, Chapman UniversityFollow
Mihaela Vajiac, Chapman University

Document Type

Article

Publication Date

2011

Abstract

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.

Comments

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

Recommended Citation

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

Peer Reviewed

1

Copyright

Springer