| 多复变函数在广义多圆柱区域上的黎曼边值问题 |
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| 引用本文： | 杨丕文. 多复变函数在广义多圆柱区域上的黎曼边值问题[J]. 四川师范大学学报(自然科学版), 1991, 0(2) |
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| 作者姓名： | 杨丕文 |
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| 作者单位： | 四川师范大学数学系 |
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| 摘 要： | 本文考察了二元复变函数的 Riemann 边值问题(边界条件 F~(++)=G_1F~(+-)+G_2F~(-+)+G_3F~(--)+f).利用二元复函数柯西型积分的索霍茨基公式,给出了当 G_i(i=1,2,3)是相应区域内不为零的二元解析函数时解的表达式;考察了 G_j=z_1~(k_(1j))z_2~(k_(2j))(k_(ij),i=1,2;j=1,2,3,是整数)时的可解情况,并将G_j 的是前一种情况时的结果推广到了方程组:W_(2_j)=gi(i=1,2)的解类.
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| 关 键 词： | 多元解析函数 黎曼边值问题 柯西型积分 |
ON RIEMANN BOUNDARY VALUE PROBLEMS FOR FUNCTIONS OF SEVERAL COMPLEX VANABVLES IN THE GENERALIZED POLYCYLINDER |
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| Yang Piwen. ON RIEMANN BOUNDARY VALUE PROBLEMS FOR FUNCTIONS OF SEVERAL COMPLEX VANABVLES IN THE GENERALIZED POLYCYLINDER[J]. Journal of Sichuan Normal University(Natural Science), 1991, 0(2) |
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| Authors: | Yang Piwen |
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| Affiliation: | Yang Piwen Department of Mathematics |
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| Abstract: | This paper investigates the Riemann boundary value problems for functions of two complex variables(boundary condi- tion:F~(++)=G_1F~(+-)+G_2F~(-+)+G_3F~(--)+f).First of all, by using the Plemelj formular,the formular of solutions of the problem is obtained when G_i(i=1,2,3)is a nonzero analytic function of two complex variable in its domain of definition, next,the author searchs for the solvebility of the problem when G_j=z_1~K_(1j)z_2~K_(2j)(K_(ij),i=1,2;j=1,2,3,is a integral number),and then extends the result of the former to the class of the solutions of following system of equations:W_=g_i(i= 1,2). |
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| Keywords: | analytic functions of several complex variables Riemann boundary value problem Cauchy type integral |
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