Kato – Kuroda Theorems for a Large Class of Perturbations

  title={Kato – Kuroda Theorems for a Large Class of Perturbations},
  author={A D Ionescu and W. Schlag},
We prove asymptotic completeness for operators of the form H = −∆+L on L(R), d ≥ 2, where L is an admissible perturbation. Our class of admissible perturbations contains multiplication operators defined by real-valued potentials V ∈ L(R), q ∈ [d/2, (d + 1)/2] (if d = 2 then we require q ∈ (1, 3/2]), as well as real-valued potentials V satisfying a global Kato condition. The class of admissible perturbations also contains first order differential operators of the form ~a · ∇−∇ ·~a for suitable… CONTINUE READING

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