Half-line Schrodinger Operators With No Bound States
Damanik, David ; Killip, Rowan
arXiv, 0303001 / Harvested from arXiv
Text on arXiv
We consider Sch\"odinger operators on the half-line, both discrete and continuous, and show that the absence of bound states implies the absence of embedded singular spectrum. More precisely, in the discrete case we prove that if $\Delta + V$ has no spectrum outside of the interval $[-2,2]$, then it has purely absolutely continuous spectrum. In the continuum case we show that if both $-\Delta + V$ and $-\Delta - V$ have no spectrum outside $[0,\infty)$, then both operators are purely absolutely continuous. These results extend to operators with finitely many bound states.
Publié le : 2003-02-28
Classification:  Mathematical Physics,  Mathematics - Spectral Theory 
@article{0303001,
     author = {Damanik, David and Killip, Rowan},
     title = {Half-line Schrodinger Operators With No Bound States},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0303001}
}

Damanik, David; Killip, Rowan. Half-line Schrodinger Operators With No Bound States. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0303001/