Orthogonal polynomials and partial differential equations on the unit ball
| dc.creator | Pinar, Miguel | |
| dc.creator | Xu, Yuan | |
| dc.date | 2007-12-19 | |
| dc.date.accessioned | 2026-07-07T08:50:16Z | |
| dc.date.available | 2026-07-07T08:50:16Z | |
| dc.description | Orthogonal polynomials of degree $n$ with respect to the weight function $W_μ(x) = (1-\|x\|^2)^μ$ on the unit ball in $\RR^d$ are known to satisfy the partial differential equation $$ [ Δ- \la x, \nabla \ra^2 - (2 μ+d) \la x, \nabla \ra \right ] P = -n(n+2 μ+d) P $$ for $μ> -1$. The singular case of $μ= -1,-2, ...$ is studied in this paper. Explicit polynomial solutions are constructed and the equation for $ν= -2,-3,...$ is shown to have complete polynomial solutions if the dimension $d$ is odd. The orthogonality of the solution is also discussed. | |
| dc.description | 9 | |
| dc.identifier | https://arxiv.org/abs/0712.3091 | |
| dc.identifier | http://arxiv.org/abs/0712.3091 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144550 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 33C50, 33E30, 42C05 | |
| dc.title | Orthogonal polynomials and partial differential equations on the unit ball | |
| dc.type | text |