Weighted L^2 polynomial approximation in C
Jujie Wu (Sun Yat-Sen University)
Abstract: We study the density of polynomials in $H^2(\Omega, \varphi)$, the space of square integrable holomorphic functions in a bounded domain $\Omega$ in $\C$, where $\varphi$ is a subharmonic function. In particular, we prove that the density holds in Caratheodory domains for any subharmonic function $\varphi$ in a neighborhood of the closure of $\Omega$. In non-Caratheodory domains, we prove that the density depends on the weight function, giving examples. We also give a weighted $L^2$ version of Weierstrass theorem and give the example. Some $L^2$ approximation in higher dimension also will be state here, which part are in progress now.
This is joint with Severine Biard and John Erik Fornaess.
complex variables
Audience: researchers in the topic
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