Second order difference equations and discrete orthogonal polynomials of two variables
| dc.creator | Xu, Yuan | |
| dc.date | 2004-07-27 | |
| dc.date.accessioned | 2026-07-07T05:10:42Z | |
| dc.date.available | 2026-07-07T05:10:42Z | |
| dc.description | The second order partial difference equation of two variables $ \CD u:= A_{1,1}(x) Δ_1 \nabla_1 u + A_{1,2}(x) Δ_1 \nabla_2 u + A_{2,1}(x) Δ_2 \nabla_1 u + A_{2,2}(x) Δ_2 \nabla_2 u & \qquad \qquad \qquad \qquad + B_1(x) Δ_1 u + B_2(x) Δ_2 u = λu, $ is studied to determine when it has orthogonal polynomials as solutions. We derive conditions on $\CD$ so that a weight function $W$ exists for which $W \CD u$ is self-adjoint and the difference equation has polynomial solutions which are orthogonal with respect to $W$. The solutions are essentially the classical discrete orthogonal polynomials of two variables. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0407447 | |
| dc.identifier | http://arxiv.org/abs/math/0407447 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72008 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42C05, 33C45 | |
| dc.title | Second order difference equations and discrete orthogonal polynomials of two variables | |
| dc.type | text |