Clifford分析中密度函数含参量的Cauchy型积分算子的性质
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摘要
在Clifford分析中利用正则函数的一些结果与广义球坐标变换,讨论了密度函数含参量的Cauchy型积分算子的H?lder连续性,并且得到了密度函数含参量的Cauchy型积分的Plemelj公式.
In this paper,we study the problem of the Cauchy-type singular integral operator for density function containing parameter.By using some known results of the regular function and the hyperspherical coordinate transformation,we get the H?lder continuity and Plemelj formula of the Cauchy-type integral operator for density function containing parameter.
In this paper,we study the problem of the Cauchy-type singular integral operator for density function containing parameter.By using some known results of the regular function and the hyperspherical coordinate transformation,we get the H?lder continuity and Plemelj formula of the Cauchy-type integral operator for density function containing parameter.
引文
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[3]BATARD T,SAINT J C,BERTHIER M.A Metric Approach to nD Images Edge Detection with Clifford Algebras[J].Journal of Mathematical Imaging and Vision,2009,33(3):296-312.
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[5]徐振远.Clifford代数上正则函数的Riemann问题[J].科学通报,1987,32(23):476-477.
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[8]HUANG S,QIAO Y Y,WEN G C.Real and Complex Clifford Analysis[M].New York:Springer,2005.
[9]王丽萍,乔玉英,乔海英.Clifford分析中一类拟Cauchy型积分算子的不动点定理及迭代构造[J].数学进展,2009,38(4):385-396.
[10]路见可.解析函数边值问题[M].武汉:武汉大学出版社,2004.
[11]赵桢.奇异积分方程[M].北京:北京师范大学出版社,1984.
[2]ROBERT P.First Order Elliptic Systems,A Function Theoretic Approach[M].New York:Academic Press,1983.
[3]BATARD T,SAINT J C,BERTHIER M.A Metric Approach to nD Images Edge Detection with Clifford Algebras[J].Journal of Mathematical Imaging and Vision,2009,33(3):296-312.
[4]BRACKX F,DELANGHE R,SOMMEN F.Clifford Analysis[M].Boston:Pitrnan Books Limited,1982.
[5]徐振远.Clifford代数上正则函数的Riemann问题[J].科学通报,1987,32(23):476-477.
[6]WEN G C.Clifford Analysis and Elliptic Systems,Hyperbolic Systems of First Order Equations[M].Beijing:Peking University Press,1990.
[7]黄沙.Clifford分析中双正则函数的非线性边值问题[J].中国科学(A辑),1996,39(3):227-236.
[8]HUANG S,QIAO Y Y,WEN G C.Real and Complex Clifford Analysis[M].New York:Springer,2005.
[9]王丽萍,乔玉英,乔海英.Clifford分析中一类拟Cauchy型积分算子的不动点定理及迭代构造[J].数学进展,2009,38(4):385-396.
[10]路见可.解析函数边值问题[M].武汉:武汉大学出版社,2004.
[11]赵桢.奇异积分方程[M].北京:北京师范大学出版社,1984.