Article

Annali di Matematica Pura ed Applicata

, Volume 190, Issue 2, pp 247-261

Bicomplex hyperfunctions

  • F. ColomboAffiliated withDipartimento di Matematica, Politecnico di Milano
  • , I. SabadiniAffiliated withDipartimento di Matematica, Politecnico di Milano Email author 
  • , D. C. StruppaAffiliated withSchmid College of Science, One University Drive, Chapman University
  • , A. VajiacAffiliated withSchmid College of Science, One University Drive, Chapman University
  • , M. VajiacAffiliated withSchmid College of Science, One University Drive, Chapman University

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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 numbers PDE systems Syzygy Resolutions Hyperfunctions Duality Dolbeault complex

Mathematics Subject Classification (2000)

16E05 35C15 13P10 35N05