Resonances for Schrödinger operators with compactly supported potentials
Journées équations aux dérivées partielles (2008), article no. 3, 18 p.

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 d1 dimensions. This note contains a sketch of the proof of our main results [5, 6] 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 include a review of previous results concerning the resonance counting functions for Schrödinger operators with compactly-supported potentials.

@article{JEDP_2008____A3_0,
     author = {Christiansen, T. J. and Hislop, P. D.},
     title = {Resonances for Schr\"odinger operators with compactly supported potentials},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2008},
     doi = {10.5802/jedp.47},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_2008____A3_0}
}
Christiansen, T. J.; Hislop, P. D. Resonances for Schrödinger operators with compactly supported potentials. Journées équations aux dérivées partielles (2008), article  no. 3, 18 p. doi : 10.5802/jedp.47. http://www.numdam.org/item/JEDP_2008____A3_0/

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