论文标题
双变量正交多项式的二次分解
Quadratic decomposition of bivariate orthogonal polynomials
论文作者
论文摘要
我们描述了两种双变量重量函数的双变量多项式序列在二次转化下的初始重量的基督教派转换方面，与几个双变量多项式序列正交。我们分析了从给定的一个正交序列的对称双变量多项式序列的构建，该序列是正交到正交定义在正面上的重量函数。在此描述中，对于所涉及的三个项矩阵系数，起着一种重要的作用。我们将其作为案例研究之间的关系，在球和单纯形上定义的对称正交多项式之间。
We describe bivariate polynomial sequences orthogonal to a symmetric weight function in terms of several bivariate polynomial sequences orthogonal with respect to Christoffel transformations of the initial weight under a quadratic transformation. We analyze the construction of a symmetric bivariate orthogonal polynomial sequence from a given one, orthogonal to a weight function defined on the positive plane. In this description plays an important role a sort of Backlund type matrix transformations for the involved three term matrix coefficients. We take as a case study relations between symmetric orthogonal polynomials defined on the ball and on the simplex.
