A dispersive estimate for the Schrödinger operator in star-shaped networks

Mathematics – Analysis of PDEs

Scientific paper

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Scientific paper

We prove time decay $L^1 ({\cal R}) \rightarrow L^\infty ({\cal R}),$ where
${\cal R}$ is an infinite star-shaped network, estimates for the Schr\"odinger
group $e^{it(- \frac{d^2}{dx^2} + V)}$ for real-valued potentials $V$ satisfy
some regularity and decay assumptions.

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