DOI QR코드

DOI QR Code

PROPERTIES OF HYPERHOLOMORPHIC FUNCTIONS ON DUAL SEDENION NUMBERS

  • Kim, Ji Eun (Department of Mathematics, Pusan National University) ;
  • Ha, Su Jin (Department of Mathematics, Pusan National University) ;
  • Shon, Kwang Ho (Department of Mathematics, Pusan National University)
  • Received : 2014.11.19
  • Accepted : 2014.11.27
  • Published : 2014.12.25

Abstract

The aim of this paper is to define hyperholomorphic functions with dual sedenion variables on $\mathcal{S}{\times}\mathcal{S}$, where $$\mathcal{S}{\sim_=}\mathbb{C}^8$$. By the condition of harmonicity, we research properties of hyperholomorphic functions of dual sedenion variables in Clifford analysis.

Keywords

References

  1. L. Hormander, An introduction to complex analysis in several variables, North-Holland, Amsterdam, 1966.
  2. H. S. Jung, S. J. Ha, K. H. Lee, S. M. Lim and K. H. Shon, Structures of hyperholomorphic functions on dual quaternion numbers, Honam Mathematical J. 35 (2013), 809-817. https://doi.org/10.5831/HMJ.2013.35.4.809
  3. J. E. Kim, S. J. Lim and K. H. Shon, Regular functions with values in ternary number system on the complex Clifford analysis, Abstract and Applied Analysis. (2013) Article ID 136120, 7 Pages.
  4. J. E. Kim, S. J. Lim and K. H. Shon, Regularity of functions on the reduced quaternion field in Clifford analysis, Abstract and Applied Analysis. (2014) Article ID 654798, 8 Pages.
  5. J. E. Kim and K. H. Shon, The regularity functionson dual split quaternions in Clifford analysis, Abstract and Applied Analysis. (2014) Article ID 369430, 8 Pages.
  6. S. G. Krantz, Funtion theory of several complex variables, Am. Math. Soc, Providence. (2001).
  7. S. J. Lim and K. H. Shon, Hyperholomorphic functions and hyperconjugate harmonic functions of octonion variables, J. Inequ. Appl. 77 (2013), 1-8.
  8. K. Nono, Hyperholomorphic functions of a quaternion variable, Bull. Fukuoka Univ. Ed. 32 (1983), 21-37.
  9. K. Nono, On the octonionic linearization of Laplacian and octonionic function theory, Bull. Fukuoka Univ. Ed. 37 (1988), 1-15.
  10. S. H. Park and K. H. Shon, Sedenion functions of hypercomplex variables in the sense of Clifford analysis, East Asian Math. J. 29(5) (2013), 521-527. https://doi.org/10.7858/eamj.2013.036