East Asian mathematical journal

  • 제32권5호
  • /
  • Pages.641-649
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  • 2016
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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REGULAR FUNCTIONS FOR DIFFERENT KINDS OF CONJUGATIONS IN THE BICOMPLEX NUMBER FIELD

  • Kang, Han Ul (Department of Mathematics, Pusan National University) ;
  • Jung, Sangsu (Department of Mathematics, Pusan National University) ;
  • Shon, Kwang Ho (Department of Mathematics, Pusan National University)
  • 투고 : 2016.04.06
  • 심사 : 2016.08.18
  • 발행 : 2016.09.30
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초록

In this paper, using three types of conjugations in a bicomplex number filed $\mathcal{T}$, we provide some basic definitions of bicomplex number and definitions of regular functions for each differential operators. And we investigate the corresponding Cauchy-Riemann systems and the corresponding Cauchy theorems in $\mathcal{T}$ in Clifford analysis.

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참고문헌

  1. H. S. Jung and K. H. Shon, Functions and Differential Operators in The Dual Reduced Quaternion Field, East Asian Math. J. 29 (2013), 293-302. https://doi.org/10.7858/eamj.2013.020
  2. H. U. Kang and K. H. Shon, Relations of L-regular Functions on Quaternions in Clifford Analysis, East Asian Math. J. 20 (2013), 667-675.
  3. J. E. Kim and K. H. Shon, Properties of Regular Functions with Values in Bicomplex Numbers, Bull. Korean Math. Soc. Preprint.
  4. S. J. Lim and K. H. Shon, Dual Quaternion Functions and Its Applications, East Asian Math. J. 28 (2012), 553-559. https://doi.org/10.7858/eamj.2012.040
  5. S. J. Lim and K. H. Shon, Dual Quaternion Functions and Its Applications, J. of Applied Mathematics Art. ID 583813 (2013), 6 pages.
  6. S. J. Lim and K. H. Shon, Hyperholomorphic Functions and Hyper-conjugate Harmonic Functions of Octonion Variables, J. of Inequalities and Applications 77 (2013), 8 pages.
  7. M. E. Luna-Elizarraras and M. Shapiro, Bicomplex Numbers and their Elementary Functions, CUBO A Mathematical J. 14 (2012), 61-80. https://doi.org/10.4067/S0719-06462012000200004
  8. M. Naser, Hyperholomorphic functions, Siberian Math. J. 12 (1971), 959-968.
  9. D. Rochon and M. Shapiro, On Algebraic Properties of Bicomplex and Hyperbolic Numbers, Anal. Univ. Oradea (2004), 28 pages.

피인용 문헌

  1. DIFFERENTIALS OF THE BICOMPLEX FUNCTIONS FOR EACH CONJUGATIONS BY THE NAIVE APPROACH vol.39, pp.2, 2016, https://doi.org/10.5831/hmj.2017.39.2.307