A Regularity Theory for Static Schrödinger Equations on \(\boldsymbol{\mathbb{R}}\) d in Spectral Barron Spaces
Ziang Chen, Jianfeng Lu, Yulong Lu, Shengxuan Zhou · SIAM Journal on Mathematical Analysis · 2023
Abstract. Spectral Barron spaces have received considerable interest recently, as it is the natural function space for approximation theory of two-layer neural networks with a dimension-free convergence rate. In this paper, we study the regularity of solutions to the whole-space static Schrödinger equation in spectral Barron spaces. We prove that if the source of the equation lies in the spectral Barron space [Formula: see text] and the potential function admitting a nonnegative lower bound decomposes as a positive constant plus a function in [Formula: see text], then the solution lies in the spectral Barron space [Formula: see text].