Weighted-𝐿² polynomial approximation in ℂ

Biard, Séverine; Fornæss, John; Wu, Jujie

doi:10.1090/tran/7935

Weighted-$L^2$ polynomial approximation in $\mathbb {C}$
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by Séverine Biard, John Erik Fornæss and Jujie Wu PDF

Trans. Amer. Math. Soc. 373 (2020), 919-938 Request permission

Abstract:

We study the density of polynomials in $H^2(\Omega ,e^{-\varphi })$, the space of square integrable holomorphic functions in a bounded domain $\Omega$ in $\mathbb {C}$, where $\varphi$ is a subharmonic function. In particular, we prove that the density holds in Carathéodory domains for any subharmonic function $\varphi$ in a neighborhood of $\overline {\Omega }$. In non-Carathéodory domains, we prove that the density depends on the weight function, giving examples.

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