Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 149, Issue 2, Pages 715-728Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/proc/15225
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Funding
- JSPS KAKENHI [19H01792, 17K18725]
- Natural Sciences and Engineering Council (NSERC) of Canada
- National Science Foundation of China [11771015]
- Grants-in-Aid for Scientific Research [19H01792, 17K18725] Funding Source: KAKEN
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The biorthogonal rational functions of F-3(2) type on the uniform grid demonstrate properties similar to classical orthogonal polynomials, with three different operators X, Y, Z describing these properties and generating a quadratic algebra akin to Askey-Wilson type attached to hypergeometric polynomials.
The biorthogonal rational functions of F-3(2) 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 X, Y, Z which are tridiagonal with respect to three distinct bases of the relevant finite-dimensional space. The pairwise commutators of the operators X, Y, Z generate a quadratic algebra which is akin to the algebras of Askey-Wilson type attached to hypergeometric polynomials.
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