An estimate of the root mean square error incurred when approximating an $f\in L^2(\mathbb{R})$ by a partial sum of its Hermite series

Mei Ling Huang, Ron Kerman, Susanna Spektor

Let $f$ be a band-limited function in $L^2(\mathbb{R})$. Fix $T>0$ and suppose $f^{\prime }$ exists and is integrable on $[-T,T]$. This paper gives a concrete estimate of the er…