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http://dx.doi.org/10.7468/jksmeb.2013.20.2.129

PROPERTIES OF HYPERHOLOMORPHIC FUNCTIONS ON DUAL TERNARY NUMBERS  

Jung, Hyun Sook (Department of Mathematics, College of Natural Sciences, Pusan National University)
Shon, Kwang Ho (Department of Mathematics, College of Natural Sciences, Pusan National University)
Publication Information
The Pure and Applied Mathematics / v.20, no.2, 2013 , pp. 129-136 More about this Journal
Abstract
We research properties of ternary numbers with values in ${\Lambda}(2)$. Also, we represent dual ternary numbers in the sense of Clifford algebras of real six dimensional spaces. We give generation theorems in dual ternary number systems in view of Clifford analysis, and obtain Cauchy theorems with respect to dual ternary numbers.
Keywords
hyperholomorphic function; ternary number; dual number system; Clifford analysis; complex differential equation;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 K. Gurlebeck and T.Q. Viet: Function spaces in complex and Clifford analysis, On some complete system of monogenic rational functions. Proc. 14h Inter. Conf. on Finite or Inf. Dimen. Complex Anal. Appl., Advances in Complex Anal. Appl. Vol. 14, Hue Univ. (2008), 156-169.
2 F. Gursey & H.C. Tze: Complex and Quaternionic Analyticity in Chiral and Gauge Theories I. Ann. of Physics 128 (1980), 29-130.   DOI   ScienceOn
3 J. Kajiwara, X.D. Li & K.H. Shon: Regeneration in Complex, Quaternion and Clifford analysis. Proc. 9th Inter. Conf. on Finite or Inf. Dimen. Complex Anal. and Appl., Advances in Complex Anal. Appl. Vol. 2, Kluwer Academic Publishers (2004), 287-298.
4 J. Kajiwara, X.D. Li & K.H. Shon: Function spaces in complex and Clifford analysis, Inhomogeneous Cauchy Riemann system of quaternion and Clifford analysis in ellipsoid. Proc. 14th Inter. Conf. on Finite or Inf. Dimen. Complex Anal. Appl., Advances in Complex Anal. Appl. Vol. 14, Hue Univ. (2008), 127-155.
5 L. Kula & Y. Yayli: Dual spilt quaternions and screw motion in Minkowski 3-space. Iranian J. Sci. Tech, Trans. A. 30 (2006), 245-258.
6 S.J. Lim & K.H. Shon: Properties of hyperholomorphic functions in Clifford analysis. East Asian Math. J. 28 (2012), 553-559.   과학기술학회마을   DOI   ScienceOn
7 S.J. Lim & K.H. Shon: Hyperholomorphic functions and hyper-conjugate harmonic functions of octonion variables. J. Inequal. Appl. 77 (2013), 1-8.
8 S.J. Lim & K.H. Shon: Regularities of functions with values in C(n) of matrix algebras M(n;C). submitted in J. Inequal. Appl. (2013).
9 M. Naser: Hyperholomorphic functions. Siberian Math. J. 12 (1971), 959-968.
10 K. Nono: Hyperholomorphic functions of a quaternion variable. Bull. Fukuoka Univ. Ed. 32 (1983), 21-37.
11 K. Nono: On the Quaternion Linearization of Laplacian. Bull. Fukuoka Univ. Ed. 35 (1985), 5-10.
12 K. Nono: Characterization of domains of holomorphy by the existence of hyper-conjugate harmonic functions. Rev. Roumaine Math. Pures Appl. 31 (1986), no. 2, 159-161.
13 K. Nono: Domains of Hyperholomorphic in ${\mathbb{C}}^2{\times}{\mathbb{C}}^2$. Bull. Fukuoka Univ. Ed. 36 (1987), 1-9.
14 A. Sudbery: Quaternionic analysis. Math. Proc. Camb. Phil. Soc. 85 (1979), 199-225.   DOI
15 F. Brackx: On (k)-monogenic functions of a quaternion variable. Res. Notes in Math. 8 (1976), 22-44.
16 F. Brackx, R. Delanghe & F. Sommen: Clifford analysis. Res. Notes in Math. 76 (1982), 1-43.
17 C.A. Deavours: The quaternion calculus. Amer. Math. Monthly 80 (1973), 995-1008.   DOI   ScienceOn