四元数分析中几类广义函数的性质
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摘要
研究了四元数分析中柯西核函数,及其引出的几类广义函数,得到了这些广义函数偏导数的表达式。作为应用,还很容易的由此推导出了T算子的几种偏导数。
The Cauchy kernel function in quaternion analysis,and several types of generalized functions related to it are considered.The representations of partial derivative of the generalized functions are obtained.As an application,it is also easy to deduce several partial derivatives of the T operator.
The Cauchy kernel function in quaternion analysis,and several types of generalized functions related to it are considered.The representations of partial derivative of the generalized functions are obtained.As an application,it is also easy to deduce several partial derivatives of the T operator.
引文
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[14]鄢盛勇.四元数分析中无界域上正则函数的带位移非线性边值问题[J].数学的实践与认识:2017,47(4):175-180.
[15] KAHLER U,MARTINS A M.Quaternionic Beltrami-type equations and homemorphic solutions[J].Advances in Applied Clifford Algebras,2001,11(S2):177-182.
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[2] BEGEHR H,DZHURAEV A.An Introduction to Several Complex Variables and Partial Differetial Equations[M].Harlow:Longman,1997.
[3]闻国椿,杨广武,黄沙,等.广义解析函数及其拓广[M].石家庄:河北教育出版社,1989.
[4] BEGEHR H,HILE G N.A Hierarchy of integral operators[J].Rocky Mountains J Math,1997,27(3):85-139.
[5] BEGEHR H.Pompeiu operators in complex hypercomplex and clifford analysis[J].Rev Roumaine Math Pures Appl,2001,46(1):1-11.
[6] GRLEBECK K,SPRSSIG W.Quaternionic analysis and elliptic boundary value problem[M].Boston:Birkh user,1990.
[7] SUDBERY A.Quaternionic Analysis[J],Math.Proc.Comb.Phil.Soc.,1979,85:199-225.
[8]杨丕文.双圆柱区域上的高阶四元数函数的Dirichlet边值问题[J].中国科学:数学,2011,41(6):485-496.
[9]杨丕文.四元数分析与偏微分方程[M].北京:科学出版社,2009.
[10]王丽萍,杨贺菊,谢永红,乔玉英.四元数分析中加权Dirac算子的Riemann边值问题[J].中国科学:数学,2015,45(11),1919-1930.
[11]鄢盛勇.四元数分析中正则函数向量的非线性边值问题[J].华南师范大学学报(自然科学版):2012,44(4):24-27.
[12]鄢盛勇.四元数分析中无界域上的Pompeiu公式和Plemelj公式[J].兰州理工大学学报:2014,40(1):155-159.
[13]鄢盛勇.四元数分析中无界域上正则函数的线性边值问题[J].西南师范大学学报(自然科学版):2015,40(2):20-25.
[14]鄢盛勇.四元数分析中无界域上正则函数的带位移非线性边值问题[J].数学的实践与认识:2017,47(4):175-180.
[15] KAHLER U,MARTINS A M.Quaternionic Beltrami-type equations and homemorphic solutions[J].Advances in Applied Clifford Algebras,2001,11(S2):177-182.
[16] GURLEBECK K,KAHLER U,SHAPIRO M.On the operator in hyperholomorphic funtion theory[J].Advances in Applied Clifford Algebras,1999,9(1):23-40.
[17] BRACKX F,DE SCHEPPER H,LUNA-ELIZARRARAS M S,et al.On fundamental solutions in Clifford analysis[J].Compl.Anal.Oper.Theory,2012,6(2):325-339.
[18] BRACKX F,DE SCHEPPER H,LUNA-ELIZARRARAS M S,et al.The Teodorescu operator in Clifford analysis[J].Chin.Ann.Math.,2012,33B(4):625-640.
[19] BRACKX F,DELANGHE R,SOMMEN F.Sphercial means,distributions and convolution operators in Clifford analysis[J].Chin.Ann.Math.,2003,24B(2):133-146.
[20]施瓦兹.广义函数论[M].北京:高等教育出版社,2010.