Dispersive Bounds for the three-dimensional Schrodinger equation with almost critical potentials

Details Dispersive Bounds for the three-dimensional Schrodinger equation with almost critical potentials Dispersive Bounds for the three-dimensional Schrodinger equation with almost critical potentials

2004-09-19

arxiv.org/abs/math/0409327v1

Geom. Funct. Anal., 16, no. 3 (2006), 517-536.

Mathematics

Analysis of PDEs

17 pages

Scientific paper

10.1007/s00039-006-0568-5

We prove a dispersive estimate for the time-independent Schrodinger operator H = -\Delta + V in three dimensions. The potential V(x) is assumed to lie in the intersection L^p(R^3) \cap L^q(R^3), p < 3/2 < q, and also to satisfy a generic zero-energy spectral condition. This class, which includes potentials that have pointwise decay |V(x)| < C(1+|x|)^{-2-\epsilon}, is nearly critical with respect to the natural scaling of the Laplacian. No additional regularity, decay, or positivity of V is assumed.

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