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An algebraic description of the bispectrality of the biorthogonal rational functions of Hahn type
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-11-30 , DOI: 10.1090/proc/15225 Satoshi Tsujimoto , Luc Vinet , Alexei Zhedanov
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-11-30 , DOI: 10.1090/proc/15225 Satoshi Tsujimoto , Luc Vinet , Alexei Zhedanov
Abstract:The biorthogonal rational functions of 
type 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 operators 
which are tridiagonal with respect to three distinct bases of the relevant finite-dimensional space. The pairwise commutators of the operators 
generate a quadratic algebra which is akin to the algebras of Askey-Wilson type attached to hypergeometric polynomials.
中文翻译：
Hahn型双正交有理函数的双谱性的代数描述
摘要：均匀网格上类型的双正交有理函数提供了具有双谱性质的有理函数的最简单示例，其与经典正交多项式的相似。这些特性由三个差分算符描述，它们相对于相关有限维空间的三个不同的底角是三对角的。算子的成对换向器生成一个二次代数，该二次代数类似于附加到超几何多项式的Askey-Wilson类型的代数。
更新日期：2021-01-11
type 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 operators which are tridiagonal with respect to three distinct bases of the relevant finite-dimensional space. The pairwise commutators of the operators generate a quadratic algebra which is akin to the algebras of Askey-Wilson type attached to hypergeometric polynomials. 中文翻译：
Hahn型双正交有理函数的双谱性的代数描述
摘要：
均匀网格上类型的双正交有理函数提供了具有双谱性质的有理函数的最简单示例，其与经典正交多项式的相似。这些特性由三个差分算符描述，它们相对于相关有限维空间的三个不同的底角是三对角的。算子的成对换向器生成一个二次代数，该二次代数类似于附加到超几何多项式的Askey-Wilson类型的代数。
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