论文标题
双光谱雅各比型多项式
Bispectral Jacobi type polynomials
论文作者
论文摘要
我们研究了雅各比型多项式的双光谱，这些双项式是高阶差分运算符的特征函数，可以通过采用固定数量连续数量的雅各比多项式的合适线性组合来定义。 Jacobi型多项式包括特殊情况，即Krall-Jacobi多项式。作为主要结果，我们证明雅各比型多项式始终满足高阶复发关系（即它们是双光谱）。我们还证明，Krall-Jacobi家族是唯一相对于实际线上的措施正交的雅各比型多项式。
We study the bispectrality of Jacobi type polynomials, which are eigenfunctions of higher-order differential operators and can be defined by taking suitable linear combinations of a fixed number of consecutive Jacobi polynomials. Jacobi type polynomials include, as particular cases, the Krall-Jacobi polynomials. As the main results we prove that the Jacobi type polynomials always satisfy higher-order recurrence relations (i.e., they are bispectral). We also prove that the Krall-Jacobi families are the only Jacobi type polynomials which are orthogonal with respect to a measure on the real line.
