乘法双准周期解析函数的一些引理*

本文证明乘法双准周期解析函数即使在区域边界上实部等于零,本身仍可能不恒为零,且指出了出现这种情况的条件,并用实例说明确实存在这种情况.最后并讨论了乘数不事先指定时间题的一般解.

Some Lemmas on Doubly Quasi-Periodic Analytic Functions in Multiplication

In this paper, some lemmas on doubly quasi-periodic analytic functions in multiplication are proved. Suchfunctions may not be identical to zero even if their real parts vanish on the boundary. Conditions for in which this case appears is also obtained. A concrete example is given to show that this case actually exists. Finally, the general solution of the considered Dirichlet problem of doubly quasi-periodic analytic functions with zero real parts on the boundary is obtained, provided the multipliers are not prescribed.