Smoothness of the fundamental solution of Schr\"odinger equations with mild trapping

Kouichi Taira

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arXiv · 2203.01499

Smoothness of the fundamental solution of Schr\"odinger equations with mild trapping

Kouichi Taira

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Abstract

In this short note, smoothness of the fundamental solution of Schr\"odinger equations on a complete manifold is studied. It is shown that (1) the fundamental solution is smooth under "mild" trapping conditions; (2) there is a Riemannian manifold which is equal to Euclidean space outside a compact set such that the fundamental solution is not smooth.

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Kouichi Taira. 2022-03-03. Smoothness of the fundamental solution of Schr\"odinger equations with mild trapping. https://arxiv.org/abs/2203.01499

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