Rigorous WKB for finite order linear recurrence relations with smooth coefficients
| dc.creator | Costin, O. | |
| dc.creator | Costin, R. D. | |
| dc.date | 2006-08-16 | |
| dc.date.accessioned | 2026-07-07T07:21:51Z | |
| dc.date.available | 2026-07-07T07:21:51Z | |
| dc.description | We study the $ε\to 0$ behavior of recurrence relations of the type $\sum_{j=0}^l a_j(kε,ε)y_{k+j}=0,$ $k\in \zdd$ ($l$ fixed). The $a_j$ are $C^{\infty}$ functions in each variable on $I\times [0,\e_0]$ for a bounded interval $I$ and $\e_0>0$. Under certain regularity assumptions we find the asymptotic behavior of the solutions of such recurrences. In typical cases there exists a fundamental set of solutions in the form $\{\exp(\epi F_m(kε,ε))\}_{m=1... l}$ where the functions $F_m$ are $C^{\infty}$ in each variable on the same domain as the $a_j$, showing in particular that the formal perturbation-series solutions are asymptotic to true solutions of these recurrences. Some applications are also briefly discussed. | |
| dc.identifier | https://arxiv.org/abs/math/0608413 | |
| dc.identifier | http://arxiv.org/abs/math/0608413 | |
| dc.identifier | SIAM.J.Math.Anal. v27 no1 (1996) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115447 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 39A10,34E20,34E15,34E10 | |
| dc.title | Rigorous WKB for finite order linear recurrence relations with smooth coefficients | |
| dc.type | text |