旋量值函数的Plemelj公式
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摘要
对比于多复变中的Bochner-Martinelli型积分的Plernelj公式,定义了艾米尔特Clifford分析中旋量值函数的Cauchy型积分及Cauchy主值积分,得到了旋量值函数的Plemelj公式,最后给出一些特殊情形的Bochner-Martinelli型积分的Plemelj公式.
In comparison with the Plemelj formulae for the Bochner-Martinelli-type integral in the function theory of several complex variables,the authors define the Cauchy-type integral and the Cauchy principal value for the spinor-valued functions in Hermite Clifford analysis,and obtain the Plemelj formulae for the spinor-valued functions.Finally,the authors figure out some Plemelj formulae for the Bochner-Martinelli-type integrals in the special cases.
In comparison with the Plemelj formulae for the Bochner-Martinelli-type integral in the function theory of several complex variables,the authors define the Cauchy-type integral and the Cauchy principal value for the spinor-valued functions in Hermite Clifford analysis,and obtain the Plemelj formulae for the spinor-valued functions.Finally,the authors figure out some Plemelj formulae for the Bochner-Martinelli-type integrals in the special cases.
引文
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[7]Xu N,Du J Y.Plemelj formula for Cauchy type integral on certain distinguished boundary in universal Clifford analysis[J].Wuhan Univ J of Natural Sciences,2007,12(3):385-390.
[8]Du J Y,Xu N,Zhang Z X.Boundary behavior of Cauchy-type integrals in Clifford analysis[J].Acta Math Sci,2009,29B(l):210-224.
[9]He F L,Du J Y.Bochner-Martenelli type formulae for spinor valued functions[J].Acta Math Sinica,2013,56(6):829-840.
[10]Brackx F,Delanghe R,Sommen F.Clifford analysis[M].London:Pitman Books Ltd,1982.
[11]Delanghe R,Sommen F,Soucek V.Clifford analysis and spinor valued functions[M].Dordrecht:Kluwer Academic Publishers,1992.
[12]Brackx F,De Schepper H,Sommen F.The Hermitian Clifford analysis toolbox[J].Adv Appl Clifford Alg,2008,18:451-487.
[13]Brackx F,Bures J,De Schepper H,et al.Fundaments of Hermitian Clifford analysis—part I:Complex structure[J].Complex Analysis Operator Theory,2007,1:341-365.
[14]Brack F,Bures J,De Schepper H,et al.Fundaments of Hermitian Clifford analysis—part II:Splitting of hamonogenic equations[J].Complex Var Elliptic Eq,2007,52(10-11):1063-1079.
[15]Eelbode D,He F L.Taylor series in Hermitian Clifford analysis[J].Compl Anal Oper Theory,2011,5(1):97-111.
[2]Kakichev B A.Character of the continuity of the boundary values of a BochnerMartenelli integral[J].Oblast Ped Inst,1960,96:105-150.
[3]Harvey F R,Lawson H B.On boundaries of complex analytic varieties I[J].Ann Math,1975,102(2):223-290.
[4]林良裕.多复变数Cauchy型积分在角点处的极限值[J].厦门大学学报:自然科学版,1986,25(2):128~134.
[5]Ifimie V.Functions hypercomplex[J].Bull Math Soc Sc R S R,1965,57(9):279-332.
[6]Du J Y.A theorem on boundary values of integrals of Cauchy-type and its applications[J].J Math,1982,2(2):115-126.
[7]Xu N,Du J Y.Plemelj formula for Cauchy type integral on certain distinguished boundary in universal Clifford analysis[J].Wuhan Univ J of Natural Sciences,2007,12(3):385-390.
[8]Du J Y,Xu N,Zhang Z X.Boundary behavior of Cauchy-type integrals in Clifford analysis[J].Acta Math Sci,2009,29B(l):210-224.
[9]He F L,Du J Y.Bochner-Martenelli type formulae for spinor valued functions[J].Acta Math Sinica,2013,56(6):829-840.
[10]Brackx F,Delanghe R,Sommen F.Clifford analysis[M].London:Pitman Books Ltd,1982.
[11]Delanghe R,Sommen F,Soucek V.Clifford analysis and spinor valued functions[M].Dordrecht:Kluwer Academic Publishers,1992.
[12]Brackx F,De Schepper H,Sommen F.The Hermitian Clifford analysis toolbox[J].Adv Appl Clifford Alg,2008,18:451-487.
[13]Brackx F,Bures J,De Schepper H,et al.Fundaments of Hermitian Clifford analysis—part I:Complex structure[J].Complex Analysis Operator Theory,2007,1:341-365.
[14]Brack F,Bures J,De Schepper H,et al.Fundaments of Hermitian Clifford analysis—part II:Splitting of hamonogenic equations[J].Complex Var Elliptic Eq,2007,52(10-11):1063-1079.
[15]Eelbode D,He F L.Taylor series in Hermitian Clifford analysis[J].Compl Anal Oper Theory,2011,5(1):97-111.