论文标题
超球多项式的连接系数，参数加倍和广义双光谱
Connection coefficients for ultraspherical polynomials with argument doubling and generalized bispectrality
论文作者
论文摘要
我们首先提出离散波方程的概括，该方程特别满足了与Alpert的多分辨率分析相对应的细化方程的矩阵系数的条目。这些条目实际上是两个离散变量的函数，它们可以用legendre多项式表示。接下来，我们将这些函数推广到超强多项式的情况下，并表明在两个离散变量中的每个变量中，这些新功能都遵守两个广义特征值问题，这构成了广义的双光谱问题。最后，我们与其他问题建立了一些联系。
We start by presenting a generalization of a discrete wave equation that is particularly satisfied by the entries of the matrix coefficients of the refinement equation corresponding to the multiresolution analysis of Alpert. The entries are in fact functions of two discrete variables and they can be expressed in terms of the Legendre polynomials. Next, we generalize these functions to the case of the ultraspherical polynomials and show that these new functions obey two generalized eigenvalue problems in each of the two discrete variables, which constitute a generalized bispectral problem. At the end, we make some connections to other problems.
