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Second order difference equations and discrete orthogonal polynomials of two variables | | Yuan Xu
; | | Date: |
27 Jul 2004 | | Subject: | Classical Analysis and ODEs MSC-class: 42C05, 33C45 | math.CA | | Abstract: | The second order partial difference equation of two variables $ CD u:= A_{1,1}(x) Delta_1
abla_1 u + A_{1,2}(x) Delta_1
abla_2 u + A_{2,1}(x) Delta_2
abla_1 u + A_{2,2}(x) Delta_2
abla_2 u & qquad qquad qquad qquad + B_1(x) Delta_1 u + B_2(x) Delta_2 u = lambda u, $ 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. | | Source: | arXiv, math.CA/0407447 | | Services: | Forum | Review | PDF | Favorites | |
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