超越整函数的正规族{f（2nz）}（英文）

Normal Families {f（2~nz）} of Transcendental Entire Functions

研究了在一给定开集G=G1∪G2内使得集族{f(2nz):n∈N}成为正规族的整函数f的存在性,并且证明了此集族恰在集合G1内有限正规而在集合G2内正规但非有限正规.

We study the existence of an entire function f in the complex plane C such that the family {f（2nz）：n∈N} forms a normal family exactly for z in a given open set G=G1∪G2.And we prove that its 2n-translated family is finitely normal exactly on G1 and normal but not finitely normal on G2.