The gaub-lucas theorem for regular quaternionic polynomials

Trends in Mathematics

Volumn 53, Issue , 2011, Pages 275-282

  Vlacci, Fabio ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Zeroes and critical points of quaternionic polynomials

Indexed keywords

EID: 84918572875     PISSN: 22970215     EISSN: 2297024X     Source Type: Book Series    
DOI: 10.1007/978-3-0346-0246-4-19     Document Type: Conference Paper

References (24)

1. L. Ahlfors, Complex analysis, McGraw-Hill, New York (1979).
2. F. Colombo, I. Sabadini, F. Sommen, D.C. Struppa, Analysis of Dirac Systems and Computational Algebra, Birkhäuser, 2004.
3. F. Colombo, G. Gentili, I. Sabadini, D. C. Struppa, Extension results for slice regular functions of a quaternionic variable. Adv. Math. 222 (2009), 1793-1808.
4. C. G. Cullen, An integral theorem for analytic intrinsic functions on quaternions. Duke Math. J. 32 (1965), 139-148.
5. R. Fueter, Die Funktionentheorie der Differentialgleichungen δu = 0 und δδu = 0 mit vier reellen Variablen. Comment. Math. Helv. 7 (1934/5), 307-330.
6. R. Fueter, Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen. Comment. Math. Helv. 8 (1935/6), 371-378.
7. G. Gentili, C. Stoppato, Power series and analyticity over the quaternions, to appear in Math. Ann.
8. G. Gentili, C. Stoppato, The open mapping theorem for quaternionic regular functions. Ann. Sc. Norm. Super. Pisa Cl. Sci. 5 (2009), 805-815.
9. G. Gentili, C. Stoppato, Zeros of regular functions and polynomials of a quaternionic variable. Michigan Math. J. 56 (2008), 655-667.
10. G. Gentili, C. Stoppato, D. C. Struppa, F. Vlacci, Recent developments for regular functions of a hypercomplex variable. Hypercomplex Analysis, Trends in Mathematics, 165-186, Birkhauser, Basel (2009).
11. G. Gentili, D. C. Struppa, A new approach to Cullen-regular functions of a quaternionic variable. C. R. Math. Acad. Sci. Paris 342 (2006), 741-744.
12. G. Gentili, D. C. Struppa, A new theory of regular functions of a quaternionic variable. Adv. Math. 216 (2007), 279-301.
13. G. Gentili, D. C. Struppa, On the multiplicity of the zeroes of polynomials with quaternionic coefficients, Milan J. Math., 76, (2008), 15-25.
14. G. Gentili-D. C. Struppa-F. Vlacci, The Fundamental Theorem of Algebra for Hamilton and Cayley numbers, Math. Z., 259, (2008), 895-902.
15. V.V. Kravchenko,M.V. Shapiro, Integral Representations for Spatial Models of Mathematical Physics, Pitman Research Notes in Mathematics Series, 351, Longman, Harlow, 1996.
16. T. Y. Lam, A first course in noncommutative rings. Graduate Texts in Mathematics, 123, Springer-Verlag, New York, 1991.
17. J. Niven Equations in quaternions, Amer. Math. Monthly 48, (1941), 654-661.
18. J. Niven The roots of a quaternion,Amer. Math. Monthly 49, (1942), 386-388.
19. A. Pogorui, M. V. Shapiro, On the structure of the set of zeros of quaternionic polynomials. Complex Variables Theory Appl. 49 (2004), no. 6, 379-389.
20. Q.I. Rahman, G. Schmeiber, Analytic Theory of Polynomials Claredon Preb, Oxford, (2002).
21. C. Stoppato, Poles of regular quaternionic functions, Complex Var. Elliptic Equ. 54 (2009), 1001-1018.
22. A. Sudbery, Quaternionic analysis. Math. Proc. Camb. Phil. Soc. 85 (1979), 199-225.
23. I. Vignozzi, Funzioni Intere sui Quaternioni: Fattorizzazioni degli Zeri, Tesi di Laurea, Università di Firenze (2008).
24. F. Vlacci, The Argument Principle for Quaternionic Regular Functions, to appear in Michigan Math. J.