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arXiv · 2010.12838

Resolvent and spectral measure for Schr\"odinger operators on flat Euclidean cones

Junyong Zhang
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Abstract

We construct the Schwartz kernel of resolvent and spectral measure for Schr\"odinger operators on the flat Euclidean cone $(X,g)$, where $X=C(\mathbb{S}_\sigma^1)=(0,\infty)\times \mathbb{S}_\sigma^1$ is a product cone over the circle, $\mathbb{S}_\sigma^1=\R/2\pi \sigma\Z$, with radius $\sigma>0$ and the metric $g=dr^2+r^2 d\theta^2$. As products, we prove the dispersive estimates for the Schr\"odinger and half-wave propagators in this setting.

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Junyong Zhang. 2020-10-24. Resolvent and spectral measure for Schr\"odinger operators on flat Euclidean cones. https://arxiv.org/abs/2010.12838

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