Thomson’s theorem on mean square polynomial approximation
Thomson’s theorem on mean square polynomial approximation
In 1991, J. E. Thomson determined completely the structure of $H^2(\mu )$, the closed subspace of $L^2(\mu )$ that is spanned by the polynomials, whenever $\mu$ is a compactly supported measure in the complex plane. As a consequence he was able to show that if $H^2(\mu )\ne L^2(\mu )$, then …