Harmonic approximation of difference operators
- For a general class of difference operators H-epsilon = T-epsilon + V-epsilon on l(2) ((epsilon Z)(d)), where V- epsilon is a multi-well potential and a is a small parameter. we analyze the asymptotic behavior as epsilon -> 0 of the (low-lying) eigenvalues and eigenfunctions. We show that the first it eigenvalues of H converge to the first it eigenvalues of the direct suns of harmonic oscillators oil R-d located at the several wells. Our proof is microlocal.
| Author details: | Markus KleinGND, Elke RosenbergerORCiD |
|---|---|
| URL: | http://www.sciencedirect.com/science/journal/00221236 |
| DOI: | https://doi.org/10.1016/j.jfa.2009.09.004 |
| ISSN: | 0022-1236 |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2009 |
| Publication year: | 2009 |
| Release date: | 2017/03/25 |
| Source: | Journal of functional analysis. - ISSN 0022-1236. - 257 (2009), 11, S. 3409 - 3453 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
