We prove the time decay estimates where is an infinite star-shaped network, for the Schrödinger group for real-valued potentials 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, Dispersive effects and high frequency behaviour for the Schrödinger equation in star-shaped networks. Port. Math. 72 (2015), no. 4, pp. 309–355DOI 10.4171/PM/1970