On 2D discrete Schrödinger operators associated with multiple orthogonal polynomials
On 2D discrete Schrödinger operators associated with multiple orthogonal polynomials
复制标题
与多个正交多项式相关的二维离散薛定谔算子
DOI：
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复制
发表时间：
2014
期刊：
影响因子：
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通讯作者：
W. Assche
中科院分区：
文献类型：
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作者：
A. Aptekarev;Maxim S. Derevyagin;W. Assche
在二维格子上引入了一类十字形差分算子。这类算子的主要特点是其形式特征向量由多个正交多项式组成。换言之，该方案将雅可比矩阵与正交多项式之间的经典联系推广到格上算子的情形。此外，我们还展示了如何从这种构造中获得2D离散薛定谔算子，并给出了一些基于已知的多重正交多项式族的显式例子。
A class of cross-shaped difference operators on a two-dimensional (2D) lattice is introduced. The main feature of the operators in this class is that their formal eigenvectors consist of multiple orthogonal polynomials. In other words, this scheme generalizes the classical connection between Jacobi matrices and orthogonal polynomials to the case of operators on lattices. Furthermore we also show how to obtain 2D discrete Schrödinger operators out of this construction and give a number of explicit examples based on known families of multiple orthogonal polynomials.