Weighted approximation in ℂ

2017/12/04 by Jujie Wu, Wu, Jujie, John Erik Fornæss +1
Mathematics · #30D20 #30E10 #30H50 #31A05 #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:30D20 #msc:30E10 #msc:30H50 #msc:31A05

paper · pdf · doi:10.48550/arxiv.1712.01086

openalex publication_date 2017/12/04 · arxiv created 2018/11/28 · arxiv updated 2018/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if \ φ_j\_j is a sequence of subharmonic functions which are increasing to some subharmonic function φ in ℂ, then the union of all the weighted Hilbert spaces H(φ_j) is dense in the weighted Hilbert space H(φ).

Related

• Weighted-L² polynomial approximation in ℂ
• Polynomial approximation in weighted Dirichlet spaces
• Approximation of m-subharmonic functions in weighted energy classes with given boundary values
• On the weighted m-energy classes
• Weighted energy class of m-subharmonic functions