Year: 2018
Type: preprint
Abstract: We study the density of polynomials in $H^2(Ω,e^{-φ})$, the space of square integrable holomorphic functions in a bounded domain $Ω$ in $\mathbb{C}$, where $φ$ is a subharmonic function. In particular, we prove that the density holds in Carathéodory domains for any subharmonic function $φ$ in a neighborhood of $\overlineΩ$. In non-Carathéodory domains, we prove that the density depends on the weight function, giving examples.
Source: arXiv (Cornell University)
Authors: Biard, Séverine, Fornæss, John Erik, Wu, Jujie
Institution: Henan University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Norges Forskningsråd
Award: G1481673436
OpenAlex ID: W2805710756