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http://dx.doi.org/10.7468/jksmeb.2016.23.1.97

DUAL QUATERNIONIC REGULAR FUNCTION OF DUAL QUATERNION VARIABLES  

KIM, JI EUN (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY)
SHON, KWANG HO (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY)
Publication Information
The Pure and Applied Mathematics / v.23, no.1, 2016 , pp. 97-104 More about this Journal
Abstract
We give representations of differential operators and rules for addition and multiplication of dual quaternions. Also, we research the notions and properties of a regular function and a corresponding harmonic function with values in dual quaternions of Clifford analysis.
Keywords
quaternion; dual number; regular function; differentiable; Clifford analysis.;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 R. Fueter: Über die analytische Darstellung der regulären Funktionen einer Quaternio-nenvariablen. Comment. math. Helv. 8 (1936), 371-378.
2 W.R. Hamilton: Elements of Quaternions. Longmans Green, London, 1866.
3 C.J. Joly: A Manual of Quaternions. Macmillan, London, 1905.
4 J. Kajiwara, X.D. Li & K.H. Shon: Regeneration in complex, quaternion and Clifford analysis. Proc. the 9th International Conf. on Finite or Infinite Dimensional Complex Analysis and Applications, Adv. Complex Anal. Appl., Kluwer Acad. Pub., Hanoi, 2 (2004), no. 9, 287-298.
5 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. the 14th International Conf. on Finite or Infinite Dimensional Complex Analysis and Applications, National Univ. Pub., Hanoi, Vietnam, Hue Univ., 14 (2006), 127-155.
6 J.E. Kim, S.J. Lim & K.H. Shon: Regular functions with values in ternary number system on the complex Clifford analysis. Abstr. Appl. Anal., Volume 2013, Artical ID 136120.
7 J.E. Kim, S.J. Lim & K.H. Shon: Regularity of functions on the reduced quaternion field in Clifford analysis. Abstr. Appl. Anal., Volume 2014, Artical ID 654798.
8 J.E. Kim & K.H. Shon: Polar Coordinate Expression of Hyperholomorphic Functions on Split Quaternions in Clifford Analysis. Adv. Appl. Clifford Alg. 25 (2015), no. 4, 915-924.   DOI
9 J.E. Kim & K.H. Shon: The Regularity of functions on Dual split quaternions in Clifford analysis. Abstr. Appl. Anal., Volume 2014, Artical ID 369430.
10 J.E. Kim & K.H. Shon: Coset of hypercomplex numbers in Clifford analysis. Bull. Korean Math. Soc. 52 (2015), no. 5, 1721-1728.   DOI
11 J.E. Kim & K.H. Shon: Inverse Mapping Theory on Split Quaternions in Clifford Analysis. To appear in Filomat (2015).
12 A. Sudbery: Quaternionic Analysis. Math. Proc. Cambridge Philos. Soc. (rev. ed.) 85 (1979), 199225.
13 P.G. Tait: An Elementary Treatise on Quaternions. Cambridge University Press, Cambridge, 1890.
14 M. Yaglom: Complex numbers in geometry. Academic Press, New York, 1968.
15 M.A.B. Deakin: Functions of a dual or duo variable. Math. Mag. 39 (1966), no. 4, 215-219.   DOI
16 C.A. Deavours: The Quaternion Calculus. Amer. Math. Monthly 80 (1973), 995-1008.   DOI
17 T. Ferdinands & L. Kavlie: A Beckman-quarles type theorem for laguerre transformations in the dual plane. RHIT Undergrad. Math. J. 10 (2009). no. 1.
18 R. Fueter: Die Funktionentheorie der Differentialgleichungen Δu = 0 und ΔΔu = 0 mit vier reellen Variablen. Comment. math. Helv. 7 (1935), 307-330.