, Volume 257, Issue 1, pp 87-117
Date: 11 Jan 2005

Dispersive Estimates for Schrödinger Operators in Dimension Two

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Abstract

We prove L 1(ℝ2)→L (ℝ2) for the two-dimensional Schrödinger operator −Δ+V with the decay rate t −1. We assume that zero energy is neither an eigenvalue nor a resonance. This condition is formulated as in the recent paper by Jensen and Nenciu on threshold expansions for the two-dimensional resolvent.

Communicated by B. Simon
The author was partially supported by the NSF grant DMS-0300081 and a Sloan Fellowship