A Dispersive Bound for Three-dimensional Schrödinger Operators with Zero Energy Eigenvalues

Abstract

We prove a dispersive estimate for the evolution of Schrödinger operators H = −∆ + V (x) in R3. The potential is allowed to be a complex-valued function belonging to Lp(R3) ∩ Lq(R3), p < 3 2 < q, so that H need not be self-adjoint or even symmetric. Some additional spectral conditions are imposed, namely that no resonances of H exist anywhere within the… (More)

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