East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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CHARACTERIZATIONS OF SEVERAL SPLIT REGULAR FUNCTIONS ON SPLIT QUATERNION IN CLIFFORD ANALYSIS

  • Kang, Han Ul (Department of Mathematics, Pusan National University) ;
  • Cho, Jeong Young (Department of Mathematics, Pusan National University) ;
  • Shon, Kwang Ho (Department of Mathematics, Pusan National University)
  • Received : 2017.04.13
  • Accepted : 2017.04.21
  • Published : 2017.05.31
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Abstract

In this paper, we investigate the regularities of the hyper-complex valued functions of the split quaternion variables. We define several differential operators for the split qunaternionic function. We research several left split regular functions for each differential operators. We also investigate split harmonic functions. And we find the corresponding Cauchy-Riemann system and the corresponding Cauchy theorem for each regular functions on the split quaternion field.

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References

  1. 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 Math. J., 35 (2013), 809-817. https://doi.org/10.5831/HMJ.2013.35.4.809
  2. H. S. Jung and K. H. Shon, Properties of hyperholomorphic functions on dual ternary numbers, J. Korean Soc. Math. Educ. Ser. B, Pure Appl. Math., 20 (2013), 129-136.
  3. H. U. Kang and K. H. Shon, Relations of L-regular functions on quaternions in Cliffiord analysis, East Asian Math. J., 31(5) (2015), 667-675. https://doi.org/10.7858/eamj.2015.047
  4. H. U. Kang, M. J. Kim and K. H. Shon, Several properties of quaternionic regular functions in Clifford analysis, Honam Mathematical J., 37 (2015) No. 4, 569-575. https://doi.org/10.5831/HMJ.2015.37.4.569
  5. J. E. Kim and K. H. Shon, The regularity of functions on dual split quaternions in Clifford analysis, Abstr. Appl. Anal., Art. ID 369430 (2014), 8 pages.
  6. J. E. Kim and K. H. Shon, Hypermeromorpy of functions on split quaternions in Clifford analysis, East Asian Math J., 31 (2015) No. 5, 653-658. https://doi.org/10.7858/eamj.2015.045
  7. J. E. Kim and K. H. Shon, Polar coordinate expression of hyperholomorphic functions on split quaternions in Clifford analysis, Adv. Appl. Clifford Algebr., 25 (2015), No. 4, 915-924. https://doi.org/10.1007/s00006-015-0541-1
  8. 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., Article ID. 136120 (2013), 7 pages.
  9. H. Koriyama, H. Mae and K. Nono, Hyperholomorphic functions and holomorphic functions in quaternionic analysis, Bull. of Fukuoka Univ. of Edu., 60 (2011), 1-9.
  10. S. J. Lim and K. H. Shon, Split hyperholomorphic function in Clifford analysis, J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math., 22 (2015), 57-63.
  11. S. J. Lim and K. H. Shon, Regular functions with values in a noncommutative algebra using Clifford analysis, Filomat, 30(7) (2016), 1747-1755. https://doi.org/10.2298/FIL1607747L
  12. M. Naser, Hyperholomorphic functions, Siberian Math., 12 (1971), 959-968.