Optimal pointwise sampling for $L^2$ approximation

Albert Cohen, Matthieu Dolbeault

Given a function $u\in L^2=L^2(D,\mu )$, where $D\subset {\mathbb{R}}^d$ and $\mu$ is a measure on $D$, and a linear subspace $V_n\subset L^2$ of dimension $n$, we show that near-best appr…