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

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 Schr\"odinger group \(e^{it(- \frac{d^2}{dx^2} + V)}\) for real-valued potentials \(V\) satisfying some regularity and decay assumptions. Further w...

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Bibliographic Details
Published in:arXiv.org 2014-06
Main Authors: Felix Ali Mehmeti, Ammari, Kaïs, Nicaise, Serge
Format: Article
Language:English
Subjects:
Decay
Initial conditions
Online Access:Get full text
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Summary: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 Schr\"odinger 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.
ISSN:2331-8422