Characterization of a regular function with values in dual quaternions
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In this paper, we provide the notions of dual quaternions and their algebraic properties based on matrices. From quaternion analysis, we give the concept of a derivative of functions and and obtain a dual quaternion Cauchy-Riemann system that are equivalent. Also, we research properties of a regular function with values in dual quaternions and relations derivative with a regular function in dual quaternions.
Abstract
In this paper, we provide the notions of dual quaternions and their algebraic properties based on matrices. From quaternion analysis, we give the concept of a derivative of functions and and obtain a dual quaternion Cauchy-Riemann system that are equivalent. Also, we research properties of a regular function with values in dual quaternions and relations derivative with a regular function in dual quaternions.
참고문헌 (13)
- S. Goto, "Regular Functions with Values in a Commutative Subalgebra C(C) of Matrix Algebra M(4;R)", Bull. Fukuoka Univ. Ed, 61(3), pp.9~15 (2012)
- J. Kajiwara, "Regeneration in complex, quaternion and Clifford analysis", Proc. the 9th International Conf. on Finite or Infinite Dimensional Complex Analysis and Applications, (9), pp.287~298 (2004), Kluwer Acad. Pub.
- J. Kajiwara, "Function spaces in complex and Clifford analysis, Inhomogeneous Cauchy Rie-mann system of quaternion and Clifford analysis in ellipsoid", Proc. the 14th Inter-national Conf. on Finite or Infinite Dimensional Complex Analysis and Applications, 14, pp.127~155 (2006)
- 김지은, "TAYLOR SERIES OF FUNCTIONS WITH VALUES IN DUAL QUATERNION", 순수 및 응용수학, 20(4), pp.251~258 (2013), 한국수학교육학회
- J.E. Kim, "Regular functions with values in ternary number system on the complex Clif-ford analysis", Abstr. Appl. Anal, pp.7~ (2013)
- J.E. Kim, "Regularity of functions on the reduced quaternion field in Clifford analysis", Abstr. Appl. Anal, pp.8~ (2014)
- J.E. Kim, "The Regularity of functions on Dual split quaternions in Clifford analysis", Abstr. Appl. Anal, pp.8~ (2014)
- H. Koriyama, "Hyperholomorphic fucntions and holomorphic func-tions in quaternionic analysis", Bull. Fukuoka Univ. Ed, 60(part III), pp.1~9 (2011)
- H. Koriyama, "On regularities of octonionic functions and holomorphic mappings", Bull. Fukuoka Univ. Ed, 60(part III), pp.11~28 (2011)
- 임수진, "Properties of hyperholomorphic functions in Clifford analysis", East Asian Mathematical Journal, 28(5), pp.553~559 (2012), 영남수학회[DOI]
- S.J. Lim, "Dual quaternion functions and its applications", J. Applied Math, pp.6~ (2013)
- M. Naser, "Hyperholomorphic functions", Silberian Math. J, 12, pp.959~968 (1971)
- K. Nono, "Hyperholomorphic functions of a quaternion variable", Bull. Fukuoka Univ. Ed, 32, pp.37~ (1983)