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The Cauchy‐Kowalewski product for bicomplex holomorphic functions
Author(s) -
De Bie H.,
Struppa D. C.,
Vajiac A.,
Vajiac M. B.
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100047
Subject(s) - holomorphic function , mathematics , extension (predicate logic) , pure mathematics , product (mathematics) , algebra over a field , cauchy distribution , cauchy's integral formula , fourier transform , mathematical analysis , cauchy problem , initial value problem , computer science , geometry , programming language
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.