On the difference equations with periodic coefficients
| dc.creator | Buslaev, Vladimir | |
| dc.creator | Fedotov, Alexander | |
| dc.date | 2002-06-13 | |
| dc.date.accessioned | 2026-07-07T04:29:15Z | |
| dc.date.available | 2026-07-07T04:29:15Z | |
| dc.description | In this paper, we study entire solutions of the difference equation $ψ(z+h)=M(z)ψ(z)$, $z\in{\mathbb C}$, $ψ(z)\in {\mathbb C}^2$. In this equation, $h$ is a fixed positive parameter and $M: {\mathbb C}\to SL(2,{\mathbb C})$ is a given matrix function. We assume that $M(z)$ is a $2π$-periodic trigonometric polynomial. We construct the minimal entire solutions, i.e. entire solutions with the minimal possible growth simultaneously as for im$z\to+\infty$ so for im$z\to-\infty$. We show that the monodromy matrices corresponding to the minimal entire solutions are trigonometric polynomials of the same order as $M$. This property relates the spectral analysis of difference Schrödinger equations with trigonometric polynomial coefficients to an analysis of finite dimensional dynamical systems. | |
| dc.description | 45 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0206020 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0206020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57085 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Complex Variables | |
| dc.subject | 39A10; 39B32 | |
| dc.title | On the difference equations with periodic coefficients | |
| dc.type | text |