An algebraic description of the bispectrality of the biorthogonal rational functions of Hahn type
An algebraic description of the bispectrality of the biorthogonal rational functions of Hahn type
复制标题
哈恩型双正交有理函数双谱性的代数描述
DOI：
10.1090/proc/15225
复制
发表时间：
2020
影响因子：
1
通讯作者：
Zhedanov Alexei
中科院分区：
文献类型：
--
作者：
Tsujimoto Satoshi;Vinet Luc;Zhedanov Alexei
均匀网格上的双正交有理函数提供了具有类似于经典正交多项式的双谱性质的有理函数的最简单的例子。这些性质由三个差分算子来描述，它们相对于相关有限维空间的三个不同的基是三对角的。算子的成对交换子生成一个二次代数，它类似于附加在超几何多项式上的Askey-威尔逊型代数。参考文献
The biorthogonal rational functions oftype on the uniform grid provide the simplest example of rational functions with bispectrality properties that are similar to those of classical orthogonal polynomials. These properties are described by three difference operatorswhich are tridiagonal with respect to three distinct bases of the relevant finite-dimensional space. The pairwise commutators of the operatorsgenerate a quadratic algebra which is akin to the algebras of Askey–Wilson type attached to hypergeometric polynomials. References