Sharp semiclassical estimates for the number of eigenvalues below a degenerate critical level
| dc.creator | Zielinski, Lech | |
| dc.date | 2007-02-22 | |
| dc.date.accessioned | 2026-07-07T07:48:14Z | |
| dc.date.available | 2026-07-07T07:48:14Z | |
| dc.description | We consider the semiclassical asymptotic behaviour of the number of eigenvalues smaller than $E$ for elliptic operators in $L\sp 2 ({\bf R}\sp d)$. We describe a method of finding remainder estimates related to the volume of the region of the phase space in which the principal symbol takes values belonging to the interval $[E'-h; E'+h]$, where $E'$ is close to $E$. This method allows to derive remainder estimates $O(h\sp {1-d})$ for a class of symbols with critical points and non-smooth coefficients. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702665 | |
| dc.identifier | http://arxiv.org/abs/math/0702665 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124425 | |
| dc.subject | Spectral Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35P20 | |
| dc.title | Sharp semiclassical estimates for the number of eigenvalues below a degenerate critical level | |
| dc.type | text |