Bicomplex hyperfunctions
type: Item
instance of: scholarly article
title: Bicomplex hyperfunctions
zbMATH Open document ID: 1226.30044
author: Fabrizio Colombo
author: Irene Sabadini
author: D. C. Struppa
author: A. Vajiac
author: M. B. Vajiac
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2011-06-03T00:00:00Z
review text: The authors continue their study of some aspects of analysis of bicomplex numbers. In their recent work [``Singularities of functions of one and several bicomplex variables'', Ark. Mat. 49, No. 2, 277--294 (2011)] they studied the singularities of holomorphic functions of bicomplex variables. Now they use the sheaf of bicomplex-valued holomorphic functions of \(n\) bicomplex variables in order to define and study hyperfunctions as their relative \(3n\)-cohomology classes. It turns out that such hyperfunctions have their supports on the Euclidean space \(\mathbb{R}^{n}\) embedded into the \(n\)-dimensional bicomplex space \(\mathbb{BC}^{n}\), which allows to construct an abstract Dolbeault complex thus providing a fine resolution for the sheaves of bicomplex holomorphic functions.
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 46F15
Mathematics Subject Classification ID: 35C15
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 35N05
zbMATH DE Number: 5903857
zbMATH Keywords: bicomplex numbers
zbMATH Keywords: PDE systems
zbMATH Keywords: syzygy
zbMATH Keywords: resolutions
zbMATH Keywords: hyperfunctions
zbMATH Keywords: duality
zbMATH Keywords: Dolbeault complex
reviewed by: M. Shapiro
MaRDI profile type: Publication
full work available at URL: s10231-010-0148-z
OpenAlex ID: W3187834840
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DOI: 10.1007/S10231-010-0148-Z
description: scientific article; zbMATH DE number 5903857