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解析函数唯一性定理之疑问

2013-08-23 14:12:48| 分类：数学 | 标签： |举报 |字号大中小订阅

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（一）定理之内容：

设函数f(z)和g(z)在区域D内解析，D的内点列{zn}(n=1、2、……)有一极限点z0属于D。如果f(zn)=g(zn)(n=1、2、……)，那么在D内，f(z)≡g(z)

（二）定理之疑问：可证明，该定理的条件是不充分的。假设f(zn)=g(zn)=A(常数)，再设一个新函数h(z)=[g(z)-A]u(z)+A，其中u(z)在区域D内解析。很明显，f(z)和h(z)满足该定理的条件，但结论不成立。

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