Dispersive bounds for the three-dimensional Schrödinger equation with almost critical potentials
نویسنده
چکیده
We prove a dispersive estimate for the time-independent Schrödinger operator H = −∆ + V in three dimensions. The potential V (x) is assumed to lie in the intersection L(R) ∩ L(R), 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−ε, 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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