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CHARACTERIZATIONS OF SEVERAL SPLIT REGULAR FUNCTIONS ON SPLIT QUATERNION IN CLIFFORD ANALYSIS

손광호|강한울|조정영
영남수학회 (Youngnam Mathematical Society)|2017.05|East Asian Mathematical Journal|제33권 제3호|pp. 309-315

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참고문헌

키워드

Clifford analysisleft-differentialsplit quaternioncorresponding split Cauchy Riemann systemdifferential of split quaternionic functionsplit Cauchy theorem
주제분류수학

초록

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 re- search several left split regular functions for each differential operators. We also investigate split harmonic functions. And we find the correspond- ing Cauchy-Riemann system and the corresponding Cauchy theorem for each regular functions on the split quaternion field.

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 re- search several left split regular functions for each differential operators. We also investigate split harmonic functions. And we find the correspond- ing Cauchy-Riemann system and the corresponding Cauchy theorem for each regular functions on the split quaternion field.

참고문헌 (12)

  1. 정현석, "Structures of Hyperholomorphic Functions on Dual Quaternion Numbers", 호남수학학술지, 35(4), pp.809~817 (2013), 호남수학회
  2. 정현숙, "Properties of hyperholomorphic functions on dual ternary numbers", 순수 및 응용수학, 20(2), pp.129~136 (2013), 한국수학교육학회
  3. 강한울, "Relations of L-regular functions on quaternions in Clifford analysis", East Asian Mathematical Journal, 31(5), pp.667~675 (2015), 영남수학회[DOI]
  4. 강한울, "Several properties of Quaternionic regular functions in Clifford Analysis", 호남수학학술지, 37(4), pp.569~575 (2015), 호남수학회
  5. J. E. Kim, "The regularity of functions on dual split quaternions in Cli ord analysis", Abstr. Appl. Anal, pp.8~ (2014)
  6. 김지은, "Hypermeromorphy of functions on split quaternions in Clifford analysis", East Asian Mathematical Journal, 31(5), pp.653~658 (2015), 영남수학회[DOI]
  7. J. E. Kim, "Polar coordinate expression of hyperholomorphic functions on split quaternions in Cli ord analysis", Adv. Appl. Cli ord Algebr, 25(4), pp.915~924 (2015)
  8. J. E. Kim, "Regular functions with values in ternary number system on the complex Cli ord analysis", Abstr. Appl. Anal, pp.7~ (2013)
  9. H. Koriyama, "Hyperholomorphic functions and holomorphic func-tions in quaternionic analysis", Bull. of Fukuoka Univ. of Edu, 60, pp.1~9 (2011)
  10. 임수진, "Split hyperholomorphic function in Clifford analysis", 순수 및 응용수학, 22(1), pp.57~63 (2015), 한국수학교육학회
  11. S. J. Lim, "Regular functions with values in a noncommutative algebra using Cli ord anal-ysis", Filomat, 30(7), pp.1747~1755 (2016)
  12. M. Naser, "Hyperholomorphic functions", Siberian Math. J, 12, pp.959~968 (1971)

관련 논문AI추천

Hypermeromorphy of functions on split quaternions in Clifford analysis김지은, 손광호영남수학회 · East Asian Mathematical Journal2015 · 제31권 제5호Relations of L-regular functions on quaternions in Clifford analysis강한울, 손광호영남수학회 · East Asian Mathematical Journal2015 · 제31권 제5호RELATIONS BETWEEN QUATERNIONIC DIFFERENTIAL AND THE CORRESPONDING CAUCHY RIEMANN SYSTEM강한울, 김민지, 손광호영남수학회 · East Asian Mathematical Journal2016 · 제32권 제3호Split hyperholomorphic function in Clifford analysis손광호, 임수진한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제1호REGULAR FUNCTIONS FOR DIFFERENT KINDS OF CONJUGATIONS IN THE BICOMPLEX NUMBER FIELD강한울, 손광호, 정상수영남수학회 · East Asian Mathematical Journal2016 · 제32권 제5호Characterizations of Functions on Dual Octonion Variables in Clifford Analysis손광호, 임수미영남수학회 · East Asian Mathematical Journal2014 · 제30권 제3호

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