复双球垒域上具有离散局部全纯核的线性奇异积分方程  

Linear Singular Integral Equation with Discrete Locally Holomorphic Kernel on a Building Domain of Complex Biballs

作　　者：阮其华[1] 林良裕[1] 

机构地区：[1]厦门大学数学系,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2001年第6期1179-1183,共5页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金资助项目 (197710 68)

摘　　要：利用 Cn空间中复双球垒域上具有离散局部全纯核的奇异积分的“椭圆”邻域挖法的柯西主值及立体角系数方法 ,讨论了一类具有相应核的线性奇异积分方程和方程组 ,证明了此奇异积分方程与一 Fredholm方程等价 ,并且其特征方程存在唯一解 .Let D be a building domain of complex biballs in C^n; L~* be a functions set which satisfies Lipschitz condition on D and can be continuously extended to D such that f∈C()∩C′(D) for all f∈L~*; Ω be a finite discrete locally holomorphic kernel; 'VP' denote cauchy principla value on the boundary D, if the neighborhood of the singular point is taken as 'ellipse', the anthers apply the composite formula ∫_(ζ∈D(γ_2))Ω(η(ζ,t))∫_(t∈D(γ_1))Ω(η(ξ,ζ))=(1-a-b)∫_(D)φ(ζ)Ω(η(ζ,t))+a(1-a)φ(t) to prove that corresponding linear singular integral equation s_1φ+t_1H_(2γ)φ+Kφ=f or P_1φ+H_(2γ)Q_1φ+Kφ=f are equivalent to the Fredholm equation or equations, and theirs characteristic equation or equations have a unique solution, where s_1, t_1, P_1, Q_1 are constants or constants matrix satisfing a^(-1)t_1~2(1-a)-s_1~2+a^(-1)s_1t_1(1-2a)≠0,a=1-α(t),t≠0, P_1Q_1=Q_1P_1, det(a^(-1)(1-a)Q_1~2-P_1~2+a^(-1)(1-2a)Q_1P_1)≠0 f∈L~*() is given and K is a Fredholm operator, H_(2r)φ=(1-α(t))^(-1)∫_(D)φΩ.

关 键 词：复双球垒域 线性奇异积分方程 离散局部全纯核 “椭圆”邻域挖法 立体角系数法 特征方程 

分 类 号：O175.5[理学—数学]