正规族与分担函数

Normal Families and Shared Functions

设a(≠0)和b(■0)是区域D上的两个全纯函数,并且在函数b的零点处a'不取0.■={f}是区域D内的一族亚纯函数,若每个f的零点都是重级的,且满足f=af'=b,则■在区域D内正规.举例说明结论成立的条件是必不可少的.

Let a and b be holomorphic functions on a plane domain D such that a has no zero, b is not zero identically, and at does not take the value 0 at the zeros of b. Let ξ = {f} be a family of meromorphic functions on D, all of whose zeros are multiple, such that f = a→←fl = b. Then the family is normal on D. Examples are given to show the necessity of the conditions.