ON THE COMPOUND BOUNDARY PROBLEM FOR DOUBLY-PERIOD WITH SHIFT

In this paper, we will discuss a kind of the compound boundary problem for doubly-period-Haseman-Carleman boundary Problem Rm with doubly-period (simply called H-C Problem Rm) :To find a doubly-periodic function φ(z) analytic in S~+ and S~- except z=0 (including the union of z= 0 with periods 2ω_1, 2ω_2) and φ(z) may have m order of singularity at z= 0, which satisfies the follow-ing boundary condition:where a(t) is sense-preserving homeomorphic mapping on L_1 and α′(t)≠0,α′(t)∈H(L_1), α(t+2n_1ω_1+     

一类带平移的奇异积分方程

本文利用解析方法,对方程的系数适合一定解析性条件下,对实轴上带平移的奇异积分方程,给出该方程的一种直接解法,并得出其可解条件,解的个数及解的表达式。     

一类带位移的双周期复合边值问题

对于带位移的复合边值问题，著作（２）中利用保角粘合与各份方程的方法进行了讨论，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同期的情况，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。