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Properties of regular functions with values in bicomplex numbers

김지은|손광호
대한수학회 (The Korean Mathematical Society)|2016.03|대한수학회보 (Bulletin of the KMS)|제53권 제2호|pp. 507-518

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참고문헌

키워드

conjugationClifford analysisCauchy-Riemann systembicomplex numberholomorphic function
주제분류수학

초록

In this paper, using forms of conjugations, we give some algebraic properties of bicomplex numbers. We research differential operators, elementary functions and the analogous Cauchy-Riemann system in bicomplex number systems. Also, we investigate the definition and properties of regular functions with values in bicomplex settings in Clifford analysis.

Abstract

In this paper, using forms of conjugations, we give some algebraic properties of bicomplex numbers. We research differential operators, elementary functions and the analogous Cauchy-Riemann system in bicomplex number systems. Also, we investigate the definition and properties of regular functions with values in bicomplex settings in Clifford analysis.

참고문헌 (20)

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  9. J. E. Kim, "Polar coordinate expression of hyperholomorphic functions on split quaternions in Clifford analysis", Adv. Appl. Clifford Algebr, 25(4), pp.915~924 (2015)
  10. 김지은, "COSET OF A HYPERCOMPLEX NUMBER SYSTEM IN CLIFFORD ANALYSIS", 대한수학회보, 52(5), pp.1721~1728 (2015), 대한수학회
  11. M. E. Luna-Elizarraras, "Bicomplex numbers and their elementary functions", Cubo Mat. Educ, 14(2), pp.61~80 (2012)
  12. G. B. Price, "An Introduction to Multicomplex Spaces and Functions" (1991), Marcel Dekker Inc.
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  14. J. Ryan, "Complexified Clifford analysis", Complex Var. Theory Appl, 1, pp.119~149 (1982)
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  16. C. Segre, "Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici", Math Ann, 40(3), pp.413~467 (1892)
  17. G. Soukhomlinoff, "Uber Fortsetzung von linearen Funktionalen in linearen komplexen Raumen und linearen Quaternionraumen", Matematicheskii Sbornik, 45(2), pp.353~358 (1938)
  18. N. Spampinato, "Estensione nel campo bicomplesso di due teoremi, del Levi-Civita e del Severi, per le funzioni olomorfe di due variabili bicomplesse I, II", Reale Accad. Naz Lincei, 22, pp.38~43 (1935)
  19. N. Spampinato, "Sulla rappresentazione di funzioni di variabile bicomplessa totalmente derivabili", Ann. Mat. Pura Appl, 14(1), pp.305~325 (1936)
  20. O. Teichmuller, "Operatoren im Waschsschen Raum", J. Rein Angew. Math, 174, pp.73~124 (1936)

관련 논문AI추천

REGULAR FUNCTIONS FOR DIFFERENT KINDS OF CONJUGATIONS IN THE BICOMPLEX NUMBER FIELD강한울, 손광호, 정상수영남수학회 · East Asian Mathematical Journal2016 · 제32권 제5호Relations of L-regular functions on quaternions in Clifford analysis강한울, 손광호영남수학회 · East Asian Mathematical Journal2015 · 제31권 제5호Exponential form of biquaternionic variables in Clifford analysis김지은, 손광호대한수학회 · 대한수학회논문집2017 · 제32권 제1호Characterization of a regular function with values in dual quaternions김지은, 손광호한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제1호DUAL QUATERNIONIC REGULAR FUNCTION OF DUAL QUATERNION VARIABLES김지은, 손광호한국수학교육학회 · 이론수학과 교직수학2016 · 제23권 제1호RELATIONS BETWEEN QUATERNIONIC DIFFERENTIAL AND THE CORRESPONDING CAUCHY RIEMANN SYSTEM강한울, 김민지, 손광호영남수학회 · East Asian Mathematical Journal2016 · 제32권 제3호

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