Strichartz Estimates for the Schroedinger Equation with Time-Periodic L^{n/2} Potentials

Details Strichartz Estimates for the Schroedinger Equation with Time-Periodic L^{n/2} Potentials Strichartz Estimates for the Schroedinger Equation with Time-Periodic L^{n/2} Potentials

2007-08-13

arxiv.org/abs/0708.1547v2

Mathematics

Analysis of PDEs

21 pages. Added L^2 stability statement to main theorem, as it was already implicit in the proof

Scientific paper

We prove Strichartz estimates for the Schroedinger operator $H = -\Delta + V(t,x)$ with time-periodic complex potentials $V$ belonging to the scaling-critical space $L^{n/2}_x L^\infty_t$ in dimensions $n \ge 3$. This is done directly from estimates on the resolvent rather than using dispersive bounds, as the latter generally require a stronger regularity condition than what is stated above. In typical fashion, we project onto the continuous spectrum of the operator and must assume an absence of resonances. Eigenvalues are permissible at any location in the spectrum, including at threshold energies, provided that the associated eigenfunction decays sufficiently rapidly.

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