A REGULARITY THEORY FOR STATIC SCHRODINGER EQUATIONS ON RN SPECTRAL BARRON SPACES.

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 Schr\odinger equation in spectral Barron spaces. We prove that if the source of the equation lies in the spectral Barron space s(d) and the potential function admitting a nonnegative lower bound decomposes as a positive constant plus a function in s(d), then the solution lies in the spectral Barron space s+2(d). [ABSTRACT FROM AUTHOR]