Bicomplex hyperfunctions

In this paper, we consider bicomplex holomorphic functions of several variables in .We use the sheaf of these functions to define and study hyperfunctions as their relative 3 n -cohomology classes. We show that such hyperfunctions are supported by the Euclidean space within the bicomplex space , and...

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Bibliographic Details
Published inAnnali di matematica pura ed applicata Vol. 190; no. 2; pp. 247 - 261
Main Authors Colombo, F., Sabadini, I., Struppa, D. C., Vajiac, A., Vajiac, M.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.05.2011
Springer Nature B.V
Subjects
Analytic functions
Euclidean geometry
Euclidean space
Homology
Mathematical analysis
Mathematics
Mathematics and Statistics
Sheaves
Resolutions
35C15
Syzygy
Bicomplex numbers
PDE systems
35N05
13P10
Dolbeault complex
16E05
Hyperfunctions
Duality
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Summary:In this paper, we consider bicomplex holomorphic functions of several variables in .We use the sheaf of these functions to define and study hyperfunctions as their relative 3 n -cohomology classes. We show that such hyperfunctions are supported by the Euclidean space within the bicomplex space , 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 3 n − 1.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-010-0148-z