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

Abstract : We prove the time decay estimates L1(R)→L∞(R), where R is an infinite star-shaped network, for the Schrödinger group eit(−d2dx2+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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https://hal-uphf.archives-ouvertes.fr/hal-03138323
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Submitted on : Thursday, February 11, 2021 - 10:01:49 AM
Last modification on : Tuesday, July 5, 2022 - 3:07:48 AM

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  • HAL Id : hal-03138323, version 1
  • ARXIV : 1204.4998

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Felix Ali Mehmeti, Kaïs Ammari, Serge Nicaise. A dispersive estimate for the Schrödinger operator in star-shaped networks. Port.Math., 2015, 72, pp.309-355. ⟨hal-03138323⟩

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