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Schrödinger dispersive estimates for a scaling-critical class of potentials

We prove a dispersive estimate for the evolution of Schroedinger operators H = -Δ+ 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.

preprint2010arXivOpen access
Marius BeceanuMichael Goldberg
math.AP
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Marius BeceanuMichael Goldberg

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