Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices

Frank, Rupert L.; Simon, Barry

Duke Math. J., Tome 156 (2011) no. 1, p. 461-493 / Harvested from Project Euclid

Résumé

We prove bounds of the form \[\sum_{e\in I\cap\sigma_{\rm d}(H)} {\rm dist} \big(e,\sigma_{\rm e} (H)\big)^{1/2}\leq L^1{\rm {-norm of a perturbation}}, \] where $I$ is a gap. Included are gaps in continuum one-dimensional periodic Schrödinger operators and finite gap Jacobi matrices, where we get a generalized Nevai conjecture about an $L^1$ -condition implying a Szegő condition. One key is a general new form of the Birman-Schwinger bound in gaps.

Publié le : 2011-04-15
Classification: 35P15, 35J10, 47B36

@article{1301678730,
     author = {Frank, Rupert L. and Simon, Barry},
     title = {Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices},
     journal = {Duke Math. J.},
     volume = {156},
     number = {1},
     year = {2011},
     pages = { 461-493},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1301678730}
}

Frank, Rupert L.; Simon, Barry. Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices. Duke Math. J., Tome 156 (2011) no. 1, pp.  461-493. http://gdmltest.u-ga.fr/item/1301678730/