A Regularity Theory for Static Schr\"odinger Equations on $\mathbb{R}^d$ in Spectral Barron Spaces. (arXiv:2201.10072v1 [math.AP])

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 $\mathcal{B}^s(\mathbb{R}^d)$ and the potential function
admitting a non-negative lower bound decomposes as a positive constant plus a
function in …

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