Hilbert空间中具有正算子系数的亚纯单叶算子值函数(英文)

MEROMORPHIC UNIVALENT OPERATOR-VALUED FUNCTIONS WITH POSITIVE OPERATOR COEFFICIENT ON HILBERT SPACE

本文讨论了 Hilbert空间中具有正算子系数的亚纯单叶算子值函数集 Σ[α,β],得到了 f( z)∈Σ[α,β]的充要条件及算子系数估计 ,并表明在算术平均及凸线性组合下Σ[α,β]是闭的 .

In this paper, we introduce the class Σ of meromorphic univalent operator-valued functions with positive operator coefficient on Hilbert space. And we obtain a sufficient and necessary condition and operator coefficient estimates for f(z)∈Σ and show that the class Σ is closed under arithmetic means and convex linear combinations.