Polynomial Approximation in $L^2$ of the Double Exponential via Complex Analysis

Pierre Bizeul, Boaz Klartag

We study the polynomial approximation problem in $L^2(\hat{I}{¼}_1)$ where $\hat{I}{¼}_1(dx)=e^{-|x|}/2dx$. We show that for any absolutely continuous function $f$, $$ \sum_{k=1}^{\infty} \log^…