Annali di Matematica Pura ed Applicata

, Volume 190, Issue 2, pp 247–261

Bicomplex hyperfunctions

  • F. Colombo
  • I. Sabadini
  • D. C. Struppa
  • A. Vajiac
  • M. Vajiac
Article

DOI: 10.1007/s10231-010-0148-z

Cite this article as:
Colombo, F., Sabadini, I., Struppa, D.C. et al. Annali di Matematica (2011) 190: 247. doi:10.1007/s10231-010-0148-z
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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.

Keywords

Bicomplex numbersPDE systemsSyzygyResolutionsHyperfunctionsDualityDolbeault complex

Mathematics Subject Classification (2000)

16E0535C1513P1035N05

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2010

Authors and Affiliations

  • F. Colombo
    • 1
  • I. Sabadini
    • 1
  • D. C. Struppa
    • 2
  • A. Vajiac
    • 2
  • M. Vajiac
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.Schmid College of Science, One University DriveChapman UniversityOrangeUSA