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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Published in | Annali di matematica pura ed applicata Vol. 190; no. 2; pp. 247 - 261 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer-Verlag
01.05.2011
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0373-3114 1618-1891 |
DOI: | 10.1007/s10231-010-0148-z |