, Volume 251, Issue 1, pp 157-178
Date: 27 Aug 2004

Dispersive Estimates for Schrödinger Operators in Dimensions One and Three

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Abstract

We consider L 1L estimates for the time evolution of Hamiltonians H=−Δ+V in dimensions d=1 and d=3 with bound We require decay of the potentials but no regularity. In d=1 the decay assumption is ∫(1+|x|)|V(x)|dx<∞, whereas in d=3 it is |V(x)|≤C(1+|x|)−3−.

Communicated by B. Simon
Supported by the NSF grant DMS-0070538 and a Sloan fellowship.