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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| Vydáno v: | Advances in mathematics (New York. 1965) Ročník 216; číslo 1; s. 279 - 301 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Inc
01.12.2007
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| Témata: | |
| ISSN: | 0001-8708, 1090-2082 |
| On-line přístup: | Získat plný text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Gentili, Graziano Struppa, Daniele C. |
| Author_xml | – sequence: 1 givenname: Graziano surname: Gentili fullname: Gentili, Graziano email: gentili@math.unifi.it organization: Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni, 67 A, Firenze, Italy – sequence: 2 givenname: Daniele C. surname: Struppa fullname: Struppa, Daniele C. email: struppa@chapman.edu organization: Department of Mathematics and Computer Science, Chapman University, Orange, CA 92866, USA |
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| Cites_doi | 10.1080/0278107042000220276 10.1007/BF01620640 10.1215/S0012-7094-60-02701-0 10.1017/S0305004100055638 10.1007/BF01292723 10.1215/S0012-7094-65-03212-6 10.1080/17476939208814584 10.1007/BF03043103 10.1080/17476930108815384 10.1016/j.crma.2006.03.015 |
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| References | Gentili, Struppa (bib006) 2006; 342 Rinehart (bib012) 1960; 27 Sudbery (bib013) 1979; 85 Fueter (bib004) 1934; 7 Leutwiler (bib010) 1992; 20 Pogorui, Shapiro (bib011) 2004; 49 Kravchenko, Shapiro (bib007) 1996; vol. 351 Colombo, Sabadini, Sommen, Struppa (bib002) 2004 Fueter (bib005) 1939; 12 Laville, Ramadanoff (bib008) 1998; 8 Laville, Ramadanoff (bib009) 2001; 45 Ahlfors (bib001) 1966 Cullen (bib003) 1965; 32 Ahlfors (10.1016/j.aim.2007.05.010_bib001) 1966 Colombo (10.1016/j.aim.2007.05.010_bib002) 2004 Leutwiler (10.1016/j.aim.2007.05.010_bib010) 1992; 20 Rinehart (10.1016/j.aim.2007.05.010_bib012) 1960; 27 Laville (10.1016/j.aim.2007.05.010_bib008) 1998; 8 Sudbery (10.1016/j.aim.2007.05.010_bib013) 1979; 85 Cullen (10.1016/j.aim.2007.05.010_bib003) 1965; 32 Fueter (10.1016/j.aim.2007.05.010_bib004) 1934; 7 Gentili (10.1016/j.aim.2007.05.010_bib006) 2006; 342 Kravchenko (10.1016/j.aim.2007.05.010_bib007) 1996; vol. 351 Fueter (10.1016/j.aim.2007.05.010_bib005) 1939; 12 Pogorui (10.1016/j.aim.2007.05.010_bib011) 2004; 49 Laville (10.1016/j.aim.2007.05.010_bib009) 2001; 45 |
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| Snippet | 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... |
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| SubjectTerms | Functions of complex variables Functions of hypercomplex variables Quaternions |
| Title | A new theory of regular functions of a quaternionic variable |
| URI | https://dx.doi.org/10.1016/j.aim.2007.05.010 |
| Volume | 216 |
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