一类带位移的双周期复合边值问题

A Compound Boundary Problemwith Shift for Doublyperiodic Analytic Function

对于带位移的复合边值问题，著作（２）中利用保角粘合与积分方程的方法进行了讨论，得出较完满的结果；在单周期的情形下，其复合边值问题可利用共形映照的方法将其转化成非周期的情况，便可加以解决；但双周期的情形，其复合边值问题则尚未讨论。本文利用积分方程理论与解析函数边值问题的方法，给出了双周期的分片全纯函数的表达式，从而讨论了一类带位移的双周期复合边值问题（双周期Ｈ－Ｃ跃度问题）的可解性。

A compound boundary problem with shift for doublyperiod is considered in this paper. At first, a integral representation for doublyperiodic function on a special region is given. Then, a compound boundary problem with shift for doublyperiod is discussed by the theory of integral equation. On some conditions, the number of the solutions and conditions of solability as well as the representation of solution are given.