含余割核奇异积分修改的反演问题

Modification of the Inversion Problem for Singular Integrals with Cosecant Kernel

针对含余割核奇异积分反演问题在指标k<0时一般无解的情况,本文提出并求解了两种修改的反演问题.而后一种修改反演问题的提法与此前类似问题颇不相同.由于运用了推广的留数定理和Bertrand型换序公式使本问题及类似问题解法得以简化.

As the inversion problem for singular integrals with cosecant kernel usually has no solution in case of index k<0, we proposed and solved two different new forms of modified inversion problem in this paper. And the second form is unprecedented in similar problems. The solutions based on the generalized residue theorem and Bertrand-Poincare formula of singular integrals, which are greatly simplified, can also be used in similar problems.