HIGHER ORDER SINGULAR INTEGRAL EQUATIONS ON COMPLEX HYPERSPHERE  

作　　者：陈吕萍 钟同德 

机构地区：[1]School of Mathematical Sciences,Xiamen University

出　　处：《Acta Mathematica Scientia》2010年第5期1785-1792,共8页数学物理学报（B辑英文版）

基　　金：supported by the Natural Science Foundation of Fujian Province of China(S0850029,2008J0206);Innovation Foundation of Xiamen University(XDKJCX20063019),;the National Science Foundation of China (10771174)

摘　　要：A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.

关 键 词：complex hypersphere Cauchy integral higher order singular integral Hadamard principal value permutation formula 

分 类 号：O175.5[理学—数学] O174.5[理学—基础数学]