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Resonances for Schrödinger operators with compactly supported potentials

T. J. ChristiansenP. D. Hislop — 2008

Journées Équations aux dérivées partielles

We describe the generic behavior of the resonance counting function for a Schrödinger operator with a bounded, compactly-supported real or complex valued potential in d 1 dimensions. This note contains a sketch of the proof of our main results [, ] that generically the order of growth of the resonance counting function is the maximal value d in the odd dimensional case, and that it is the maximal value d on each nonphysical sheet of the logarithmic Riemann surface in the even dimensional case. We...

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