Abstract
We prove optimal high-frequency resolvent estimates for self-adjoint operators of the form \({G=\left(i\nabla+b(x)\right)^2+V(x)}\) on \({L^2({\bf R}^n), n\ge 3}\) , where the magnetic potential b(x) and the electric potential V(x) are long-range and large. As an application, we prove dispersive estimates for the wave group \({{\rm e}^{it\sqrt{G}}}\) in the case n = 3 for potentials b(x), V(x) = O(|x|−2-δ) for \({|x|\gg 1}\) , where δ > 0.
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Communicated by Jan Derezinski.
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Cardoso, F., Cuevas, C. & Vodev, G. High Frequency Resolvent Estimates for Perturbations by Large Long-range Magnetic Potentials and Applications to Dispersive Estimates. Ann. Henri Poincaré 14, 95–117 (2013). https://doi.org/10.1007/s00023-012-0178-8
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DOI: https://doi.org/10.1007/s00023-012-0178-8