论文标题
$ n \ times n $矩阵时间 - /频段限制示例
$N\times N$ Matrix Time-/Band- Limiting examples
论文作者
论文摘要
自1980年代以来，已经研究了正交多项式的时间和频段限制。它涉及找到具有特殊交换性能的差异或差异操作员。最近，该主题已被推广到案例中，即正交多项式是基质值。导致具有矩阵系数的差异或差异操作员。到目前为止，此类运营商的唯一明确示例是$ 2 \ times 2 $矩阵。在本文中，我们给出了许多$ n \ times n $示例和反例，以说明强大的皮尔森方程在查找此类示例中可以扮演的角色。
Time- and band-limiting in the context of orthogonal polynomials has been studied since the 1980's. It involves finding differential or difference operators with special commutative properties. More recently this topic has been generalized to the cases were the orthogonal polynomials are matrix-valued. Leading to differential or difference operators with matrix coefficients. So far the only explicit examples of such operators were $2\times 2$ matrices. In this paper we give a number of $N\times N$ examples and a counterexample to illustrate the role that strong Pearson equations can play in finding such examples.
