Dispersive estimates for the three-dimensional Schrödinger equation with rough potentials
نویسنده
چکیده
The three-dimensional Schrödinger propogator e , H = −△+V , is a bounded map from L to L∞ with norm controlled by |t|−3/2 provided the potential satisfies two conditions: An integrability condition limiting the singularities and decay of V , and a zero-energy spectral condition on H . This is shown by expressing the spectral measure of H in terms of its resolvents and proving a family of L mapping estimates for the resolvents. Previous results in this direction had required V to satisfy explicit pointwise bounds.
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تاریخ انتشار 2008