双周期解析函数的变态DIRICHLET问题

双周期解析函数的变态DIRICHLET问题 ON THE MODIFIED DIRICHLET PROBLEMS OF DOUBLY-PERIODIC ANALYTIC FUNCTIONS 路见可 Lu Jianke (Chien-ke Lu) first-author 本文考虑基本胞腔中有若干个"洞"的双周期变形Dirichlet问题,即要求一双周期解析函数,使它在"洞"的边界上其实部为已给函数,但可差一常数项。类似的加法双准周期解析函数的问题也讨论了,其加数事先给定或否均可。这些问题都得到了解决。 Le-t be a set of Liapunov contours, exterior to ore another, in the fundamental cell of double periodicities 2ω 1 , 2ω 2 , and S- be the region bounded exteriorly by L o and its periodic congruent contours. Given a real function f（t）∈H（Holder condition） on L o , the modified Dirichlet problem of a doubly-periodic analytic function φ-（z） in S- satisfying Reφ-（t） =f（t）+λ（t）, t∈L o , （1） is considered, where λ（t）=λ 3 is an undetermined real constant when t∈L o3 （but λ o =0）.The similar problem for a doubly quasi-periodic analytic function φ-（z） is also considered, with φ - （z+2ω j ）=φ - （z）+a j ,j=1, 2, where a 1 , a 2 are complex constants, preassigned or not, or Rea 1 , Rea 2 to be preassigned. One of the typical results may be stated as follows. Theorem. The modified Dirichlet problem of a doubly quasi-periodic analytic function in S- with Rea 1 , Rea 2 preassigned is always uniquely solvable. The methods used in this paper are based on those in [1, 2]. 中国科学院科学基金 1984-04-01 2021-04-01 4