Sunyer-i-Balaguer的几乎椭圆函数与Yosida的正规函数
Sunyer-i-Balaguer's Almost Elliptic Functions and Yosida's Normal Functions
摘要：
研究了复平面上两类亚纯函数的性质。第一类是Sunyer-i-Balaguer意义下的几乎椭圆函数类。这是一类亚纯函数f，使得移位族f（z+h）（h是复数）关于整个复平面的一致收敛性正规。给出了两个复数序列是某类几乎椭圆函数的零点和极点的充分条件。这些条件使一个给（第一次）明确的非平凡的例子几乎椭圆函数。第二类由K.Yosida引入，他称之为第一类的一类正规函数。这是一类亚纯函数f，使得移位族f（z+h）关于复平面上λ的一致收敛性正规，且族中没有极限点是常数函数。本文给出了两个复数序列成为第一类正规函数的零点和极点的充要条件，并得到了这类函数的零点和极点的参数表示.
英文摘要：
We study the properties of two classes of meromorphic functions in the complex plane. The first one is the class of almost elliptic functions in the sense of Sunyer-i-Balaguer. This is the class of meromorphic functions f such that the family of shifts f(z+h) (h are complex numbers) is normal with respect to the uniform convergence in the whole complex plane. Given two sequences of complex numbers, we provide sufficient conditions for them to be zeros and poles of some almost elliptic function. These conditions enable one to give (for the first time) explicit non-trivial examples of almost elliptic functions. The second class was introduced by K.Yosida, who called it a class of normal functions of the first category. This is the class of meromorphic functions f such that the family of shifts f(z+h)is normal with respect to the uniform convergence on compacta in the complex plane and no limit point of the family is a constant function. We give necessary and sufficient conditions for two sequences of complex numbers to be zeros and poles of some normal function of the first category and obtain a parametric representation for this class in terms of zeros and poles.
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