Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013, Article ID 136120, 7 pages
http://dx.doi.org/10.1155/2013/136120
Research Article

Regular Functions with Values in Ternary Number System on the Complex Clifford Analysis

Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea

Received 21 October 2013; Accepted 5 December 2013

Academic Editor: Junesang Choi

Copyright © 2013 Ji Eun Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Fueter, “Die funktionentheorie der differentialgleichungen Δu=0 und ΔΔu=0 mit vier reellen variablen,” Commentarii Mathematici Helvetici, vol. 7, no. 1, pp. 307–330, 1935. View at Publisher · View at Google Scholar · View at Scopus
  2. C. A. Deavours, “The quaternion calculus,” The American Mathematical Monthly, vol. 80, pp. 995–1008, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. Sudbery, “Quaternionic analysis,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 85, no. 2, pp. 199–224, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. M. Naser, “Hyperholomorphic functions,” Silberian Mathematical Journal, vol. 12, pp. 959–968, 1971. View at Google Scholar
  5. H. Koriyama, H. Mae, and K. Nôno, “Hyperholomorphic functions and holomorphic functions in quaternionic analysis,” Bulletin of Fukuoka University of Education, vol. 60, pp. 1–9, 2011. View at Google Scholar · View at MathSciNet
  6. K. Nôno, “Hyperholomorphic functions of a quaternion variable,” Bulletin of Fukuoka University of Education, vol. 32, pp. 21–37, 1983. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. E. Cho, “De moivre's formula for quaternions,” Applied Mathematics Letters, vol. 11, no. 6, pp. 33–35, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S. J. Sangwine and N. L. Bihan, “Quaternion polar representation with a complex modulus and complex argument inspired by the cayley-dickson form,” Advances in Applied Clifford Algebras, vol. 20, no. 1, pp. 111–120, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. R. Fueter, “Die theorie der regulären funktionen einer quaternionenvariablen,” in Comptès Rendus du Congrès International des Mathèmaticiens, Oslo 1936, vol. 1, pp. 75–91, 1935. View at Google Scholar
  10. F. Brackx, R. Delanghe, and F. Sommen, Clifford Analysis, vol. 76 of Research Notes in Mathematics, 1982.
  11. S. J. Lim and K. H. Shon, “Hyperholomorphic fucntions and hyperconjugate harmonic functions of octonion variables,” Journal of Inequalities and Applications, vol. 77, pp. 1–8, 2013. View at Google Scholar
  12. S. J. Lim and K. H. Shon, “Dual quaternion functions and its applications,” Journal of Applied Mathematics, vol. 2013, Article ID 583813, 6 pages, 2013. View at Publisher · View at Google Scholar
  13. S. J. Lim and K. H. Shon, “Regularity of functions with values in a non-commutative algebra of complex matrix algebras,” Preprint.