Generic asymptotics of resonance counting function for Schr\"odinger point interactions
Albeverio, Sergio ; Karabash, Illya M.
arXiv, 1803.06039 / Harvested from arXiv
Text on arXiv
We study the leading coefficient in the asymptotical formula $ N (R) = \frac{W}{\pi} R + O (1) $, $ R \to \infty $, for the resonance counting function $ N (R)$ of Schr\"odinger Hamiltonians with point interactions. For such Hamiltonians, the Weyl-type and non-Weyl-type asymptotics of $N (R)$ was introduced recently in a paper by J. Lipovsk\'y and V. Lotoreichik (2017). In this note, we prove that the Weyl-type asymptotics is generic.
Publié le : 2018-03-15
Classification:  Mathematics - Spectral Theory,  Mathematical Physics,  35B34, 35P20 (Primary), 35J10, 05C90, 81Q37, 81Q80 (Secondary) 
@article{1803.06039,
     author = {Albeverio, Sergio and Karabash, Illya M.},
     title = {Generic asymptotics of resonance counting function for Schr\"odinger
  point interactions},
     journal = {arXiv},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1803.06039}
}

Albeverio, Sergio; Karabash, Illya M. Generic asymptotics of resonance counting function for Schr\"odinger
  point interactions. arXiv, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/1803.06039/