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Abstract: We describe the generic behavior of the resonance counting function for aSchr\-odinger operator with a bounded, compactly-supported real or complexvalued potential in $d \geq 1$ dimensions. This note contains a sketch of theproof of our main results \cite{ch-hi1,ch-hi2} that generically the order ofgrowth of the resonance counting function is the maximal value $d$ in the odddimensional case, and that it is the maximal value $d$ on each nonphysicalsheet of the logarithmic Riemann surface in the even dimensional case. Weinclude a review of previous results concerning the resonance countingfunctions for Schr\-odinger operators with compactly-supported potentials.



Author: T. J. Christiansen, P. D. Hislop

Source: https://arxiv.org/







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