Vekua-Type Systems Related to Two-Sided Monogenic Functions

被引:0
作者
Dixan Peña Peña
Frank Sommen
机构
[1] University of Aveiro,Department of Mathematics
[2] Ghent University,Department of Mathematical Analysis
来源
Complex Analysis and Operator Theory | 2012年 / 6卷
关键词
Clifford algebras; Two-sided monogenic functions; Vekua systems; Bessel functions; 30G35; 33C10;
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学科分类号
摘要
Solutions to the Dirac equation are obtained by considering functions of axial type. This indeed gives rise to Vekua-type systems that can be solved in terms of special functions. In this paper we investigate axial symmetry for the solutions of the two-sided monogenic system and we give examples involving Bessel functions.
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页码:397 / 405
页数:8
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共 15 条
  • [1] Clifford W.K.(1878)Applications of Grassmann’s extensive algebra Am. J. Math. 1 350-358
  • [2] Fueter R.(1935)Die funktionentheorie der differentialgleichungen Δ Commun. Math. Helv. 7 307-330
  • [3] Kou K.I.(2002) = 0 und ΔΔ Methods Appl. Anal. 9 273-289
  • [4] Qian T.(1983) = 0 mit vier variablen Complex Var. Theory Appl. 2 139-150
  • [5] Sommen F.(2009)Generalizations of Fueter’s theorem Complex Var. Elliptic Equ. 54 429-440
  • [6] Lounesto P.(2010)Axially symmetric vector fields and their complex potentials J. Math. Anal. Appl. 365 29-35
  • [7] Bergh P.(1957)Monogenic Gaussian distribution in closed form and the Gaussian fundamental solution Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. 23 220-225
  • [8] Peña Peña D.(1984)Fueter’s theorem: the saga continues Rend. Circ. Mat. Palermo 6 259-269
  • [9] Sommen F.(1988)Osservazioni sulle serie di potenze nei moduli quadratici J. Math. Anal. Appl. 130 110-133
  • [10] Peña Peña D.(2000)Plane elliptic systems and monogenic functions in symmetric domains Z. Anal. Anwendungen 19 899-902