Resonances for Schrödinger operators with compactly supported potentials

T. J. Christiansen[1]; P. D. Hislop[2]

  • [1] Department of Mathematics , University of Missouri, Columbia, Missouri 65211 USA
  • [2] Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027, USA

Journées Équations aux dérivées partielles (2008)

  • page 1-18
  • ISSN: 0752-0360

Abstract

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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 [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.

How to cite

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Christiansen, T. J., and Hislop, P. D.. "Resonances for Schrödinger operators with compactly supported potentials." Journées Équations aux dérivées partielles (2008): 1-18. <http://eudml.org/doc/10635>.

@article{Christiansen2008,
abstract = {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.},
affiliation = {Department of Mathematics , University of Missouri, Columbia, Missouri 65211 USA; Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027, USA},
author = {Christiansen, T. J., Hislop, P. D.},
journal = {Journées Équations aux dérivées partielles},
language = {eng},
month = {6},
pages = {1-18},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Resonances for Schrödinger operators with compactly supported potentials},
url = {http://eudml.org/doc/10635},
year = {2008},
}

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
DA - 2008/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 18
AB - 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.
LA - eng
UR - http://eudml.org/doc/10635
ER -

References

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