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Journal Articles Portugaliae Mathematica Year : 2015

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.

Dates and versions

hal-03138323 , version 1 (23-08-2022)

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Felix Ali Mehmeti, Kaïs Ammari, Serge Nicaise. A dispersive estimate for the Schrödinger operator in star-shaped networks. Portugaliae Mathematica, 2015, 72 (4), pp.309-355. ⟨10.4171/PM/1970⟩. ⟨hal-03138323⟩
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