Properties of hyperholomorphic functions and integrals for commutative-quaternionic valued functions

Volume 11, Issue 4, pp 469--476 http://dx.doi.org/10.22436/jnsa.011.04.03

Publication Date: March 13, 2018 Submission Date: September 12, 2017 Revision Date: January 24, 2018 Accteptance Date: January 25, 2018

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2070 Downloads
• 3902 Views

Authors

Ji Eun Kim - Department of Mathematics, Dongguk University, Gyeongju, Republic of Korea.

Abstract

We give representations and properties of a hyperholomorphic function with values in commutative-quaternions. We first consider expressions of commutative-quaternions. Also, we investigate the results of derivatives and integrations for a hyperholomorphic function of commutative-quaternionic variables in Clifford analysis.

Share and Cite

Keywords

• Hyperholomorphic function
• commutative-quaternions
• Cauchy-Riemann system
• Clifford analysis

MSC

•  32A99
•  32W50
•  30G35
•  11E88

References

• [1] P. Fjelstad, S. G. Gal , n-dimensional hyperbolic complex numbers, Adv. Appl. Clifford Algebras, 8 (1998), 47–68.
  • View Article
  • MathSciNet
  • Google Scholar


• [2] R. Fueter , Analytische funktionen einer quaternionenvariablen , Comment. Math. Helv., 4 (1932), 9–20.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] J. D. Grant, I. A. B. Strachan , Hypercomplex Integrable Systems, Nonlinearity, 12 (1999), 1247–1261.
  • View Article
  • MathSciNet
  • Google Scholar


• [4] W. R. Hamilton, On quaternions; or on a new system of imaginaries in algebra , Lond. Edin. Dublin Phil. Mag. J. Sci., 25 (1944), 58–60
  • View Article
  • Google Scholar


• [5] ] J. Kajiwara, Z. Li, K. H. Shon, Function spaces in complex and Clifford analysis, Hue University, Vietnam (2006)
  • Google Scholar


• [6] D. Kaledin , Integrability of the twistor space for a hypercomplex manifold, Selecta Math., 4 (1998), 271–278.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] J. E. Kim, S. J. Lim, K. H. Shon, Regularity of functions on the reduced quaternion field in Clifford analysis, Abstr. Appl. Anal., 2014 (2014), 8 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [8] J. E. Kim, K. H. Shon, The Regularity of functions on Dual split quaternions in Clifford analysis, Abstr. Appl. Anal., 2014 (2014 ), 8 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [9] J. E. Kim, K. H. Shon , Polar coordinate expression of hyperholomorphic functions on split quaternions in Clifford analysis, Adv. Appl. Clifford Algebr., 25 (2015), 915–924.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] V. V. Kravchenkov, Applied Quaternion Analysis, Helderman, Berlin (2003)
  • Google Scholar


• [11] K. Nôno , Hyperholomorphic functions of a quaternion variable , Bull. Fukuoka Univ. Ed. III, 32 (1982), 21–37.
  • MathSciNet
  • Google Scholar


• [12] S. Olariu , Complex numbers in n dimensions , North-Holland Publishing Co., Amsterdam (2002)
  • MathSciNet


• [13] K. Scheicher, R. F. Tichy, K. W. Tomantschger , Elementary Inequalities in Hypercomplex Numbers , Anz. Österreich. Akad. Wiss. Math.-Natur. Kl., 134 (1997), 3–10
  • MathSciNet
  • Google Scholar
  • MATH


• [14] A. Sudbery , Quaternionic Analysis, Math. Proc. Cambridge Philos. Soc., 85 (1979), 199-224
  • View Article
  • Google Scholar