2022/02/24 by Guangfu Cao, Cao, Guangfu, Haichou Li +1
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2202.12112
openalex publication_date 2022/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As continuation of the study of polynomial approximation and composition operators on Dirichlet spaces of unit disk, which has settled a problem posed by Cima in 1976, the present paper aims to consider the case of the unbounded domains, such as the half-plane. Specifically, we may obtain the rational approximations in the Dirichlet spaces and characterize the composition operators which has dense range on the Dirichlet spaces over the half-plane. Moreover, this paper also considers the relationship between the Dirichlet spaces and Hardy spaces on half-plane.