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 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 in the odd dimensional case, and that it is the maximal value 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}, eid = {3}, pages = {1--18}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2008}, doi = {10.5802/jedp.47}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.47/} }
TY - JOUR AU - Christiansen, T. J. AU - Hislop, P. D. TI - Resonances for Schrödinger operators with compactly supported potentials JO - Journées équations aux dérivées partielles PY - 2008 SP - 1 EP - 18 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.47/ DO - 10.5802/jedp.47 LA - en ID - JEDP_2008____A3_0 ER -
%0 Journal Article %A Christiansen, T. J. %A Hislop, P. D. %T Resonances for Schrödinger operators with compactly supported potentials %J Journées équations aux dérivées partielles %D 2008 %P 1-18 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.47/ %R 10.5802/jedp.47 %G en %F 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/articles/10.5802/jedp.47/
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