带位移非线性奇异积分方程的离散近似解

ON DISCRETE APPROXIMATE SOLIUTON OF NONLINEAR SINGULAR INTEGRAL EQUATIONS WITH A SHIFT

将积分区间划分为2N 等分后,我们定义了带位移的离散奇异算子■^(N).对于广义 Hilder 空间 H_(α,β,γ)中的函数 u(x),被带位移奇异算子作用后与■(N)_u 的差在分点处是 O((ln N)/(Nγ)).算子■(N)是一致有界的。利用它,我们给出了一类带位移的非线性奇异积分(哥西核)

In this paper discrete singular opertor with a shift——(?)(?)^(N) would bedefined.It is uniformly bounded in the generalized Holder's space and the L_pspace.Using (?)(?)^(N),we have given the discrete approximate solution ofnonlinear singular integral(with Cauchy's kernel)equations with a shift.