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Presented By: Differential Equations Seminar - Department of Mathematics

Differential Equations Seminar: Dispersion for Coulomb waves

Adam Black (Yale)

We study the Schroedinger equation with a repulsive Coulombic potential on R^3. For radial data, we obtain a pointwise dispersive estimate with the natural decay rate of 3/2. Our proof uses the spectral theory of strongly singular potentials to obtain an expression for the evolution kernel. A semiclassical turning point analysis of the kernel then allows the time decay to be extracted via oscillatory integral estimates. This is joint work with E. Toprak, B. Vergara, and J. Zou.

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