대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제35권3호
  • /
  • Pages.825-841
  • /
  • 2020
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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CHARACTERIZATION THEOREMS OF RILEY TYPE FOR BICOMPLEX HOLOMORPHIC FUNCTIONS

  • 투고 : 2019.09.14
  • 심사 : 2020.01.16
  • 발행 : 2020.07.31
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초록

We characterize bicomplex holomorphic functions from several estimates. Originally, Riley [5] studied such problems in local case. In our study, we treat global estimates on various unbounded domains. In many cases, we can determine the explicit form of a function.

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참고문헌

  1. M. E. Luna-Elizarraras, C. O. Perez-Regalado, and M. Shapiro, On the bicomplex Gleason-Kahane-Zelazko theorem, Complex Anal. Oper. Theory 10 (2016), no. 2, 327-352. https://doi.org/10.1007/s11785-015-0455-x
  2. M. E. Luna-Elizarraras, M. Shapiro, D. C. Struppa, and A. Vajiac, Bicomplex holomorphic functions, Frontiers in Mathematics, Birkhauser/Springer, Cham, 2015. https://doi.org/10.1007/978-3-319-24868-4
  3. Y. Matsui and Y. Sato, Generalized self-inversive bicomplex polynomials with respect to the j-conjugation, submitted.
  4. G. B. Price, An introduction to multicomplex spaces and functions, Monographs and Textbooks in Pure and Applied Mathematics, 140, Marcel Dekker, Inc., New York, 1991.
  5. J. D. Riley, Contributions to the theory of functions of a bicomplex variable, Tohoku Math. J. (2) 5 (1953), 132-165. https://doi.org/10.2748/tmj/1178245302