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We construct the Schwartz kernel of resolvent and spectral measure forSchr\"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 productcone 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 thedispersive estimates for the Schr\"odinger and half-wave propagators in thissetting.

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