论文标题
梯子运算符和第二个 - 订单差方程，用于一般离散的Sobolev正交多项式
Ladder operators and a second--order difference equation for general discrete Sobolev orthogonal polynomials
论文作者
论文摘要
我们考虑涉及Hahn差异运算符的一般离散的Sobolev内部产品，因此其中包括良好的差异运算符$ \ Mathscr {d} _ {q} $和$δ$，并且作为限制情况，衍生词运算符。目标是双重的。一方面，我们为相应的非标准正交多项式构造了梯子算子，并获得了这些多项式满足的第二个阶差方程。另一方面，我们在更一般的框架中工作时，在文献中概括了一些相关的结果。此外，我们将证明可以明确计算这些构造中涉及的所有功能。
We consider a general discrete Sobolev inner product involving the Hahn difference operator, so this includes the well--known difference operators $\mathscr{D}_{q}$ and $Δ$ and, as a limit case, the derivative operator. The objective is twofold. On the one hand, we construct the ladder operators for the corresponding nonstandard orthogonal polynomials and we obtain the second--order difference equation satisfied by these polynomials. On the other hand, we generalise some related results appeared in the literature as we are working in a more general framework. Moreover, we will show that all the functions involved in these constructions can be computed explicitly.
