A Notation and preliminaries

We introduce notation and preliminary results regarding finite differences, Sobolev spaces, the Legendre basis, the Fourier basis, trigonometric polynomial interpolation and neural network approximation theory. A.1 Overview of used notation Table 1: Glossary of used notation. Let d, ` 2 N and let k d/2+`. All results are adaptations from results in [15]. The following two lemmas address the approximation of univariate monomials and the multiplication operator.