On Harrell-Stubbe Type Inequalities for the Discrete Spectrum of a Self-Adjoint Operator
| dc.creator | Ashbaugh, Mark S. | |
| dc.creator | Hermi, Lotfi | |
| dc.date | 2007-12-28 | |
| dc.date.accessioned | 2026-07-07T08:51:38Z | |
| dc.date.available | 2026-07-07T08:51:38Z | |
| dc.description | We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the Cauchy-Schwarz inequality--is used to produce ``parameter-free'', ``projection-free'' versions of their theorems. We also analyze the strength of the various inequalities that ensue. The results contain classical bounds for the eigenvalues. Extensions of a variety of inequalities à la Harrell-Stubbe are illustrated for both geometric and physical problems. | |
| dc.description | 42 pages | |
| dc.identifier | https://arxiv.org/abs/0712.4396 | |
| dc.identifier | http://arxiv.org/abs/0712.4396 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145003 | |
| dc.subject | Spectral Theory | |
| dc.subject | Differential Geometry | |
| dc.subject | 35P15; 47A75; 49R50; 58J50 | |
| dc.title | On Harrell-Stubbe Type Inequalities for the Discrete Spectrum of a Self-Adjoint Operator | |
| dc.type | text |