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arXiv · 1204.4998

Dispersive effects and high frequency behaviour for the Schrödinger equation in star-shaped networks

Felix Ali Mehmeti·Kaïs Ammari·Serge Nicaise
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Abstract

We prove the time decay estimates $L^1({\cal R}) \rightarrow L^\infty ({\cal R}),$ where ${\cal R}$ is an infinite star-shaped network, for the Schrödinger group $e^{it(- \frac{d^2}{dx^2} + V)}$ for real-valued potentials $V$ satisfying some regularity and decay assumptions. Further we show that the solution for initial conditions with a lower cutoff frequency tends to the free solution, if the cutoff frequency tends to infinity.

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Felix Ali Mehmeti, Kaïs Ammari, Serge Nicaise. 2014-06-03. Dispersive effects and high frequency behaviour for the Schrödinger equation in star-shaped networks. https://arxiv.org/abs/1204.4998

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