摘要
设F是区域D内的一亚纯函数族,k是任一正整数,M为一正数,对于F中的每个函数f,只有至少t级零点,当1 k 4时,t=k+1,当k 5时,t=k.置L(f)(z)=f(k)(z)+ak-1(z)f(k-1)(z)+…+a1(z)f′(z)+a0(z)f(z)+b(z),a(z)≠0,a0(z),a1(z),…,ak-1(z),b(z)为D内的全纯函数,则有(i)若f(z)L(f)(z)=a(z)|L(f)(z)|<M,z∈D,则F在D内正规.(ii)若f(z)L(f)(z)=a(z)|f(z)|>M,z∈D,则F在D内正规.
Let F be a family of functions meromorphic on the plane domain D. Let k be a positive integer and M be a positive constant. Suppose that for each f in F its zeros have multiplicity at least t, when 1≤k≤4, t = k + 1 and when k≥5,t=k. Set L(f)(z)=f^(k)(z)+ak-1(z)^(k-1)(z)+…+a1(z)f(z)+a0(z)f(z)+b(z), where a(z)≠0,a0(z),a1(z),…,ak-1(z),b(z) be holomorphic functions on D. Then F is normal on D if f(z)L (f)(z) = a(z)=〉|L(f)(z)|〈M for z in U or f(z)L(f)(z) = a(z)=〉|f(z)|〉M for z in D.
出处
《成都信息工程学院学报》
2007年第6期747-749,共3页
Journal of Chengdu University of Information Technology
关键词
亚纯函数
微分多项式
正规族
meromorphic function
differential polynomial
normal family