Dispersive Estimates for Matrix Schrödinger Operators in Dimension Two
نویسندگان
چکیده
We consider the non-selfadjoint operator H = [ −∆ + μ− V1 −V2 V2 ∆− μ+ V1 ] where μ > 0 and V1, V2 are real-valued decaying potentials. Such operators arise when linearizing a focusing NLS equation around a standing wave. Under natural spectral assumptions we obtain L(R)× L(R)→ L∞(R2)× L∞(R2) dispersive decay estimates for the evolution ePac. We also obtain the following weighted estimate ‖wePacf‖L∞(R2)×L∞(R2) . 1 |t| log(|t|) ‖wf‖L1(R2)×L1(R2), |t| > 2, with w(x) = log(2 + |x|).
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