A new theory of regular functions of a quaternionic variable

In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows a classical idea of Cullen, but we use a more geometric formulation to show that it is possible to build a rather complete theory. Our theor...

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Vydané v:Advances in mathematics (New York. 1965) Ročník 216; číslo 1; s. 279 - 301
Hlavní autori: Gentili, Graziano, Struppa, Daniele C.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 01.12.2007
Predmet:
Functions of complex variables
Functions of hypercomplex variables
Quaternions
Quaternions
Functions of hypercomplex variables
Functions of complex variables
ISSN:0001-8708, 1090-2082
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Shrnutí:In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows a classical idea of Cullen, but we use a more geometric formulation to show that it is possible to build a rather complete theory. Our theory allows us to extend some important results for polynomials in the quaternionic variable to the case of power series.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2007.05.010