The Cauchy-Kowalewski product for bicomplex holomorphic functions

In this paper we study the Cauchy‐Kowalewski extension of real analytic functions satisfying a system of differential equations connected to bicomplex analysis, and we use this extension to study the product in the space of bicomplex holomorphic functions. We also show how these ideas can be used to...

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Bibliographic Details
Published inMathematische Nachrichten Vol. 285; no. 10; pp. 1230 - 1242
Main Authors De Bie, H., Struppa, D. C., Vajiac, A., Vajiac, M. B.
Format Journal Article
LanguageEnglish
Published Germany WILEY-VCH Verlag 01.07.2012
WILEY‐VCH Verlag
Subjects
35A10
Bicomplex numbers
Cauchy-Kowalewski extension
holomorphicity
MSC 30G35
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Summary:In this paper we study the Cauchy‐Kowalewski extension of real analytic functions satisfying a system of differential equations connected to bicomplex analysis, and we use this extension to study the product in the space of bicomplex holomorphic functions. We also show how these ideas can be used to define a Fourier transform for bicomplex holomorphic functions.
Bibliography:ArticleID:MANA201100047
istex:CBCCF92496C4B6E7E8014F687218BFEBAC7F2BC5
ark:/67375/WNG-X7D5LHDQ-6
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201100047