A Dispersive Bound for Three-Dimensional Schrà dinger Operators with Zero Energy Eigenvalues

摘要

We prove a dispersive estimate for the evolution of Schrödinger operators H = −Δ + V(x) in 3. The potential is allowed to be a complex-valued function belonging to L p (3) ∩ L q (3), , 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 interval [0, ∞) and that eigenfunctions at zero (including generalized eigenfunctions) decay rapidly enough to be integrable.