Preservation of the absolutely continuous spectrum of Schr\"odinger equation under perturbations by slowly decreasing potentials and a.e. convergence of integral operators
Kiselev, Alexander
arXiv, 9610216 / Harvested from arXiv
Text on arXiv
We prove new criteria of stability of the absolutely continuous spectrum of one-dimensional Schr\"odinger operators under slowly decaying perturbations. As applications, we show that the absolutely continuous spectrum of the free and periodic Schr\"odinger operators is preserved under perturbations by all potentials $V(x)$ satisfying $|V(x)| \leq C(1+x)^{-\frac{2}{3}-\epsilon}.$ The main new technique includes an a.e.\ convergence theorem for a class of integral operators.
Publié le : 1996-09-30
Classification:  Mathematics - Spectral Theory,  Mathematical Physics 
@article{9610216,
     author = {Kiselev, Alexander},
     title = {Preservation of the absolutely continuous spectrum of Schr\"odinger
  equation under perturbations by slowly decreasing potentials and a.e.
  convergence of integral operators},
     journal = {arXiv},
     volume = {1996},
     number = {0},
     year = {1996},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9610216}
}

Kiselev, Alexander. Preservation of the absolutely continuous spectrum of Schr\"odinger
  equation under perturbations by slowly decreasing potentials and a.e.
  convergence of integral operators. arXiv, Tome 1996 (1996) no. 0, . http://gdmltest.u-ga.fr/item/9610216/