|
|||||
|
|
Eigenvalue estimates for Schrödinger operators on metric trees |
|
| Authors: | Tomas Ekholm Rupert L Frank Hynek Kova?ík |
| Institution: | aDepartment of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden;bDepartment of Mathematics, Fine Hall, Princeton University, Princeton, NJ 08544, USA;cDipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy |
| Abstract: | We consider Schrödinger operators on radial metric trees and prove Lieb–Thirring and Cwikel–Lieb–Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show that the bounds are valid in the endpoint case and reflect the correct order in the weak or strong coupling limit. |
| Keywords: | Schrö dinger operator Metric tree Eigenvalue estimate Lieb&ndash Thirring inequality Cwikel&ndash Lieb&ndash Rozenblum inequality |
| 本文献已被 ScienceDirect 等数据库收录！ | |