一类奇异积分算子的广义逆及其证明

Proof of Generalized Inverse for A Class of Singular Integral Operators

根据开口弧段上奇异积分方程解在端点处的不同要求,选取合适的权函数并构造一类Banach空间及奇异积分算子.讨论了该奇异积分算子的广义逆,为后续开口弧段上奇异积分方程的逼近解法求解提供了基础.

According to different requirements of solution at the end points of singular integral equation on an open arc,an appropriate weight function was determined and a class of Banach spaces and singular integral operators was constructed.Discussion of the generalized inverse of the singular integral operator has laid a foundation for future approximate solutions of singular integral equations on an open arc.