Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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STRUCTURES OF HYPERHOLOMORPHIC FUNCTIONS ON DUAL QUATERNION NUMBERS

  • Jung, Hyun Sook (Department of Mathematics, Pusan National University) ;
  • Ha, Su Jin (Department of Mathematics, Pusan National University) ;
  • Lee, Kwang Ho (Department of Mathematics, Pusan National University) ;
  • Lim, Su Mi (Department of Mathematics, Pusan National University) ;
  • Shon, Kwang Ho (Department of Mathematics, Pusan National University)
  • Received : 2013.11.22
  • Accepted : 2013.12.04
  • Published : 2013.12.25
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Abstract

We research properties of a corresponding Cauchy theorem of hyperholomorphic functions in an open set of product complex spaces, in the sense of complex Clifford analysis.

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References

  1. Futer, R., U ber die analytische Darstellung der refularen Funktionen einer Quaternionen-variablen, Comment. Math. Helv. 8 (1935), 371-378. https://doi.org/10.1007/BF01199562
  2. Gursey, F. and Tze, H.C., Complex and Quaternionic Analyticity in Chiral and Gauge Theories I, Ann. of Physics 128 (1980), 29-130. https://doi.org/10.1016/0003-4916(80)90056-1
  3. Hamilton, W.R., Hamilton's discovery of quaternions, Math. Mag. 49 (1976), 227-234. https://doi.org/10.2307/2689449
  4. Kajiwara, J., Li, X.D. and Shon, K.H., Regeneration in complex, Quaternion And Clifford analysis, Lecture Notes in Pure and Applied Mathematics. Marcel Dekker. Inc., 214 (2000), 287-298.
  5. Kajiwara, J., Li, X.D. and Shon, K.H., Function spaces in complex and Clifford analysis, Inhomogeneous Cauchy Riemann system of quaternion and Clifford analysis, Proc. the 14th International Conference on Finite or Infinite Dimensional Complex Analysis and Application. Hue. Viet Nam. Hue University 14 (2006), 127-155
  6. Oka, K., Sur les fonctions analytiques de plusieurs variables complexes. IV. Domaines d'holomorphie et domaines rationellement convexes, Jap. J. Math. 17 (1941), 517-521.
  7. Oka, K., Sur les fonctions analytiques de plusieurs variables complexes. II. Domaines d'holomorphie, J. Sci. Hiroshima Univ. 7 (1937), 115-130.
  8. Oka, K., Sur les fonctions analytiques de plusieurs variables complexes. III. Deuxieme probleme de Cousin, J. Sci. Hiroshima Univ. 9 (1939), 7-19.
  9. Oka, K., Sur les fonctions analytiques de plusieurs variables complexes. VI. Domaines pseudoconvexes, Tohoku Math. J. 49 (1942), 15-22.
  10. Oka, K., Sur les fonctions analytiques de plusieurs variables complexes. VII. Sur quelques notions arithme tiques, Bull. Soc. Math. France 78 (1950), 1-27.
  11. Oka, K., Sur les fonctions analytiques de plusieurs variables complexes. IX. Domaines finis sans point critique interieur, Jap. J. Math. 23 (1953), 97-155. https://doi.org/10.4099/jjm1924.23.0_97
  12. Oka, K., Sur les fonctions analytiques de plusieurs variables complexes. I. Domaines convexes par rapport aux fonctions rationelles, J. Sci. Hiroshima Univ. 6 (1936), 245-255.
  13. Oka, K., Sur les fonctions analytiques de plusieurs variables complexes. V. L'integrale de Cauchy, Jap. J. Math. 17 (1941), 525-531.
  14. Weil, A., L'integrale de Cauchy et les fonctions de plusieurs variables, Math. Ann. 111 (1935), 178-182. https://doi.org/10.1007/BF01472212

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