复分析中的复杂性
Complexity in complex analysis
摘要：
我们证明了平面上n连通区域的经典核函数和域函数都是由一个复变数的三个或更少的全纯函数的有理组合给出的。我们刻画了那些域的经典功能是由一个复变数的只有两个或更少的功能的合理组合。这样的区域原来有这样的性质，即它们的经典域函数都延伸到一个紧凑的黎曼曲面上的亚纯函数，这个条件将被证明是等价的条件，一个Ahlfors映射和它的衍生物是代数相关的。我们还展示了有多少这些结果可以推广到有限的黎曼曲面。
英文摘要：
We show that the classical kernel and domain functions associated to an n-connected domain in the plane are all given by rational combinations of three or fewer holomorphic functions of one complex variable. We characterize those domains for which the classical functions are given by rational combinations of only two or fewer functions of one complex variable. Such domains turn out to have the property that their classical domain functions all extend to be meromorphic functions on a compact Riemann surface, and this condition will be shown to be equivalent to the condition that an Ahlfors map and its derivative are algebraically dependent. We also show how many of these results can be generalized to finite Riemann surfaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
