Browse > Article
http://dx.doi.org/10.7858/eamj.2015.013

HYPER-CONJUGATE HARMONIC FUNCTION OF CONIC REGULAR FUNCTIONS IN CONIC QUATERNIONS  

Kim, Ji Eun (Department of Mathematics, Pusan National University)
Shon, Kwang Ho (Department of Mathematics, Pusan National University)
Publication Information
East Asian mathematical journal / v.31, no.1, 2015 , pp. 127-134 More about this Journal
Abstract
We give a rth conic regular functions with conic quaternion variables in $\mathbb{C}^2$ and obtain a hyper-conjugate harmonic function of conic regular function in conic quaternions in the sense of Clifford analysis.
Keywords
hyper-conjugate harmonic function; pseudoconvex domain; conic quaternion; Cauchy-Riemann system;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 C. A. Deavours, The quaternion calculus, Amer. Math. Monthly 80 (1973), 995-1008.   DOI   ScienceOn
2 J. Kajiwara, X. D. Li, and K. H. Shon, Regeneration in Complex, Quaternion and Clifford analysis, Proc. the 9th(2001) Internatioal Conf. on Finite or Infinite Dimensional Complex Analysis and Applications, Advances in Complex Analysis and Its Applications Vol. 2, Kluwer Academic Publishers (2004), 287-298.
3 J. Kajiwara, X. D. Li and K. H. Shon, Function spaces in Complex and Clifford Analysis, Inhomogeneous Caychy Riemann system of quaternion and Clifford analysis in ellipsoid, Proc. the 14th Internatioal Conf. on Finite or Infinite Dimensional Complex Analysis and Applications, Hue, Viet Nam, Hue Univ., 14 (2006), 127-155.
4 J. E. Kim, S. J. Lim and K. H. Shon, Taylor series of functions with values in dual quaternion, J. Korean Soc. Math. Educ., Ser. B, Pure Appl. Math. 20 (2013), no. 4, 251-258.   과학기술학회마을   DOI   ScienceOn
5 J. E. Kim, S. J. Lim and K. H. Shon, Regular functions with values in ternary number system on the complex Clifford analysis, Abstr. Appl. Anal. 2013, Article ID. 136120 (2013), 7 pages.
6 J. E. Kim, S. J. Lim and K. H. Shon, Regularity of functions on the reduced quaternion field in Clifford analysis, Abstr. Appl. Anal. 2014 Article ID. 654798 (2014), 8 pages.
7 J. E. Kim and K. H. Shon, The Regularity of functions on Dual split quaternions in Clifford analysis, Abstr. Appl. Anal. 2014 Article ID. 369430 (2014), 8 pages.
8 H. Koriyama, H. Mae, K. Nono, Hyperholomorphic Fucntions and Holomorphic Functions in Quaternionic Analysis, Bull. Fukuoka Univ. Education, 60 part III (2011), 1-9.
9 S. G. Krantz, Function theory of several complex variables, AMS Providence, Rhode Island, (2001).
10 S. J. Lim and K. H. Shon, Hyperholomorphic fucntions and hyperconjugate harmonic functions of octonion variables, J. Inequal. Appl. 77 (2013), 1-8.
11 S. J. Lim and K. H. Shon, Dual quaternion functions and its applications, J. Appl. Math. Article ID. 583813 (2013), 6 pages.
12 C. Muses, Hypernumbers and their Spaces: a Summary of New Findings, J. Study. Consciousness 5 (1972), 251-256.
13 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.
14 C. Muses, HypernumbersII. further concepts and computational applications, Appl. Math. Comput. 4 (1978), 45-66.   DOI   ScienceOn
15 M. Naser, Hyperholomorphic functions, Siberian Math. J. 12 (1971), 959-968.
16 K. Nono, Hyperholomorphic functions of a quaternion variable, Bull. Fukuoka Univ. Ed. 32 (1983), 21-37.
17 K. Nono, Domains of Hyperholomorphic in ${\mathbb{C}}^2$ ${\time}$ ${\mathbb{C}}^2$, Bull. Fukuoka Univ. Ed. 36 (1987), 1-9.
18 A. Sudbery, Quaternionic analysis, Math. Proc. Camb. Phil. Soc., 85 (1979), 199-225.   DOI