The paper by Ronald DeVore and Amos Ron addresses the approximation of a general $d$-variate function $f$ using shifts of a fixed function $\phi$ by points $\xi \in \Xi \subset \mathbb{R}^d$. The authors focus on the case where the set $\Xi$ is arbitrary, which is more realistic in many applications compared to the more studied case where $\Xi$ is a dilate of the integer lattice. They establish approximation theorems that reflect the local density of the points in $\Xi$, providing error bounds that improve in regions with higher density. The paper is divided into two main parts. The first part assumes that the set $\Xi$ is fixed and derives results showing improved approximation in regions with high density. The second part allows the centers to be chosen based on the function $f$, focusing on nonlinear approximation. The authors discuss how to choose these centers optimally and provide estimates for the approximation error. The authors also analyze two specific examples: univariate splines and surface splines. For univariate splines, they verify the assumptions and derive error estimates. For surface splines, they provide a detailed analysis of the assumptions and derive error bounds. The paper concludes with a discussion on wavelet decompositions and their use in characterizing smoothness spaces, particularly Triebel-Lizorkin spaces. They also present a method for approximating functions with lower smoothness using an "interpolation of operators" argument, decomposing the function into a smooth part and a nonsmooth part.The paper by Ronald DeVore and Amos Ron addresses the approximation of a general $d$-variate function $f$ using shifts of a fixed function $\phi$ by points $\xi \in \Xi \subset \mathbb{R}^d$. The authors focus on the case where the set $\Xi$ is arbitrary, which is more realistic in many applications compared to the more studied case where $\Xi$ is a dilate of the integer lattice. They establish approximation theorems that reflect the local density of the points in $\Xi$, providing error bounds that improve in regions with higher density. The paper is divided into two main parts. The first part assumes that the set $\Xi$ is fixed and derives results showing improved approximation in regions with high density. The second part allows the centers to be chosen based on the function $f$, focusing on nonlinear approximation. The authors discuss how to choose these centers optimally and provide estimates for the approximation error. The authors also analyze two specific examples: univariate splines and surface splines. For univariate splines, they verify the assumptions and derive error estimates. For surface splines, they provide a detailed analysis of the assumptions and derive error bounds. The paper concludes with a discussion on wavelet decompositions and their use in characterizing smoothness spaces, particularly Triebel-Lizorkin spaces. They also present a method for approximating functions with lower smoothness using an "interpolation of operators" argument, decomposing the function into a smooth part and a nonsmooth part.