Schrödinger dispersive estimates for a scaling-critical class of potentials

Details Schrödinger dispersive estimates for a scaling-critical class of potentials Schrödinger dispersive estimates for a scaling-critical class of potentials

2010-09-27

arxiv.org/abs/1009.5285v1

Mathematics

Analysis of PDEs

10 pages

Scientific paper

We prove a dispersive estimate for the evolution of Schroedinger operators H = -\Delta + V(x) in three dimensions. The potential should belong to the closure of bounded compactly-supported functions with respect to the golbal Kato norm. Some additional spectral conditions are imposed, namely that no resonances or eigenfunctions of H exist anywhere on the positive half-line. The proof is an application of a new version of Wiener's L^1 inversion theorem.

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