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 $d\ge 1$ 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.
@incollection{JEDP_2008____A3_0, author = {T. J. Christiansen and P. D. Hislop}, title = {Resonances for {Schr\"odinger} operators with compactly supported potentials}, booktitle = {}, series = {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 = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.47/} }
TY - JOUR AU - T. J. Christiansen AU - P. D. Hislop 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 - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.47/ DO - 10.5802/jedp.47 LA - en ID - JEDP_2008____A3_0 ER -
%0 Journal Article %A T. J. Christiansen %A P. D. Hislop %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 https://proceedings.centre-mersenne.org/articles/10.5802/jedp.47/ %R 10.5802/jedp.47 %G en %F JEDP_2008____A3_0
T. J. Christiansen; P. D. Hislop. Resonances for Schrödinger operators with compactly supported potentials. Journées équations aux dérivées partielles (2008), article no. 3, 18 p. doi : 10.5802/jedp.47. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.47/
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