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.