Carleman定理的推广和应用

在一含有全纯函数的零点的分段光滑封闭曲线上，深入讨论了Carleman定理的推广，由计算亚纯函数的留数和有关的函数的积分，并取它们的实部得到了形式上与原来的定理一致的结果，再将该定理应用于其他定理中，证明了它是正确的.

Generalization and Application of Carleman's Theorem

This paper intensively discussed the generalization of Carleman's theorem on a piecewise smooth closed curve which contains zeroes of the holomorphil function.By calculating the residues of a meromorphic function and a relative integrals of the function and taking their real part,we get the uniform result with primitive theorem in form,thus we apply this theorem to the other theorem again to illustrate it.