半平面中有限阶解析函数的因子分解

与经典有限阶整函数的Hadamard因子分解定理和半平面中属于Hardy空间的解析函数的内外函数的因子分解类似,对右半平面中有限阶ρ解析函数f,可以分解为三个解析函数G,eQ和eg的乘积GeQeg,其中G是一个加权Blaschke乘积,Q是一个次数不超过ρ的多项式以及eg是一个加权外函数,log|G|,ReQ和Reg-log|f|在右半平面的边界恒为零．

Factorization of Analytic Function of Finite Order in a Half-Plane

Analogous to the classic Hadamard factorization theorem about an entire function of finite order and the inner and outer factorization theorem about analytic function of the Hardy space in a half-plane, we obtain that an analytic function / of finite order p in a right half-plane can be factorized into the product GeQeg of the three analytic functions, G, eQ and eg, where G is a weighted Blaschke product, Q is a polynomial of degree not greater than p and eg is a weighted outer function such that the functions log |G|, Re Q and Reg -log |f| are identically zero in the boundary of the right half-plane.