Darboux transforms on Band Matrices, Weights and associated Polynomials
| dc.creator | Adler, Mark | |
| dc.creator | van Moerbeke, Pierre | |
| dc.date | 2000-10-27 | |
| dc.date | 2001-04-18 | |
| dc.date.accessioned | 2026-07-07T05:33:06Z | |
| dc.date.available | 2026-07-07T05:33:06Z | |
| dc.description | Classically, it is well known that a single weight on a real interval leads to orthogonal polynomials. In "Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems", Comm. Math. Phys. 207, pp. 589-620 (1999), we have shown that $m$-periodic sequences of weights lead to "moments", polynomials defined by determinants of matrices involving these moments and $2m+1$-step relations between them, thus leading to $2m+1$-band matrices $L$. Given a Darboux transformations on $L$, which effect does it have on the $m$-periodic sequence of weights and on the associated polynomials ? These questions will receive a precise answer in this paper. The methods are based on introducing time parameters in the weights, making the band matrix $L$ evolve according to the so-called discrete KP hierarchy. Darboux transformations on that $L$ translate into vertex operators acting on the $τ$-function. | |
| dc.description | 43 pages | |
| dc.identifier | https://arxiv.org/abs/nlin/0010048 | |
| dc.identifier | http://arxiv.org/abs/nlin/0010048 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79886 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | Mathematical Physics | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Darboux transforms on Band Matrices, Weights and associated Polynomials | |
| dc.type | text |