实Clifford分析中无界域上超正则函数的Cauchy型积分公式和Plemelj公式
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摘要
本文讨论了实Clifford分析中超正则函数在无界域上的Cauchy型积分公式,并把超正则函数在有界域上的Plemelj公式和Cauchy-Pompeiu公式推广到了无界域上。还讨论了无界域上的格林型公式及其几个推论。
In this paper, we discuss the Cauchy-type integral formula of hypermonogenic functions on unbounded domains in real Clifford analysis, and we extend the Plemelj formula and Cauchy-Pompeiu formula of hypermonogenic functions on bounded domains to unbounded domains, we also deal with the Green-type formula on unbounded domains and get several corollaries.
In this paper, we discuss the Cauchy-type integral formula of hypermonogenic functions on unbounded domains in real Clifford analysis, and we extend the Plemelj formula and Cauchy-Pompeiu formula of hypermonogenic functions on bounded domains to unbounded domains, we also deal with the Green-type formula on unbounded domains and get several corollaries.
引文
[1] Robert P.Gilbert, First Order Elliptic Systems, ACADEMIC PRESS 1983.
[2] Brackx F, Delanghe R, Sommen F. Clifford Analysis. In: Research Note in Mathematics 76. London: Pitman Book Ltd, 1982.
[3] Sirkka-Liisa Eriksson and Heinz Leutwiler, Hypermonogenic Functions in Clifford Algebras and their Applications in Mathematical Physics, Volum2, Birkhauser. Boston, 2000, 287-302.
[4] Sirkka-Liisa Eriksson and H.Leutwiler, Hypermonogenic Functionsand and their Cauchy-Type Theorems. In Advances in Analysis and Geometry. Trends in Mathematics Birkhauser, Basel, (2004), 97-112.
[5] Sirkka-Liisa Eriksson, Integral Formulas for Hypermonogenic Functions, Bull. Bel. Math. Soc. 11(2004), 705-717.
[6] Edwin Franks and John Ryan, Bounded Monogenic Functions on Unbounded Domains. Contemporary Mathematics. 1998-American Mathematical Socity.
[7] Wen Guochun. Clifford annalysis and elliptic system, hyperbolic systems of first order equations. World Scientific (Singapore). 1991, 230-237.
[8] 黄沙.Clifrord分析中双正则函数的一个非线性边值问题.中国科学,1996,16(1):60-64:1996,39(3):1152-1164(英文版).
[9] 乔玉英.双正则函数的非线性带位移边值问题,系统科学与数学,1999,19(4),484-489.
[10] Qiao Yuying, A boundary value problem for hypermonogenic functions in Clifford analysis, Science in China Ser. A Mathematics 2005 Vol.48 Supp.324-332.
[11] 乔玉英.广义双正则函数的非线性带位移边值问题,系统科学与数学,22(1)(2002,1),43-49.
[12] R.S.Krauβhar, Yuying Qiao, and John Ryan, Harmonic, Monogenic and Hypermonogenic Functions on Some Conformally Flat Manifolds in R~n arising from Special Arthmetic Groups of the Vahlen Group, Contemporary Mathematics, Volume 370, 2005.
[2] Brackx F, Delanghe R, Sommen F. Clifford Analysis. In: Research Note in Mathematics 76. London: Pitman Book Ltd, 1982.
[3] Sirkka-Liisa Eriksson and Heinz Leutwiler, Hypermonogenic Functions in Clifford Algebras and their Applications in Mathematical Physics, Volum2, Birkhauser. Boston, 2000, 287-302.
[4] Sirkka-Liisa Eriksson and H.Leutwiler, Hypermonogenic Functionsand and their Cauchy-Type Theorems. In Advances in Analysis and Geometry. Trends in Mathematics Birkhauser, Basel, (2004), 97-112.
[5] Sirkka-Liisa Eriksson, Integral Formulas for Hypermonogenic Functions, Bull. Bel. Math. Soc. 11(2004), 705-717.
[6] Edwin Franks and John Ryan, Bounded Monogenic Functions on Unbounded Domains. Contemporary Mathematics. 1998-American Mathematical Socity.
[7] Wen Guochun. Clifford annalysis and elliptic system, hyperbolic systems of first order equations. World Scientific (Singapore). 1991, 230-237.
[8] 黄沙.Clifrord分析中双正则函数的一个非线性边值问题.中国科学,1996,16(1):60-64:1996,39(3):1152-1164(英文版).
[9] 乔玉英.双正则函数的非线性带位移边值问题,系统科学与数学,1999,19(4),484-489.
[10] Qiao Yuying, A boundary value problem for hypermonogenic functions in Clifford analysis, Science in China Ser. A Mathematics 2005 Vol.48 Supp.324-332.
[11] 乔玉英.广义双正则函数的非线性带位移边值问题,系统科学与数学,22(1)(2002,1),43-49.
[12] R.S.Krauβhar, Yuying Qiao, and John Ryan, Harmonic, Monogenic and Hypermonogenic Functions on Some Conformally Flat Manifolds in R~n arising from Special Arthmetic Groups of the Vahlen Group, Contemporary Mathematics, Volume 370, 2005.