Factorial-type Schur functions, orthogonal rational functions, and discrete dressing chains. (English) Zbl 1379.37123
The aim of this paper is to clarify a relationship between orthogonal rational functions and discrete-time integrable systems (discrete dressing chains). It is shown that orthogonal rational functions can be constructed using a multiparameter deformation of the Schur functions, referred to by the authors as factorial-type Schur functions (since they are an extension of the factorial Schur functions). Properties of the factorial-type Schur functions are then used to derive spectral equations for the orthogonal rational functions. The compatibility condition of the spectral equations then leads to a discrete dressing chain, this being a Toda-type discrete-time integrable system describing dressing transformations for orthogonal rational functions.
Reviewer: Andrew Pickering (Madrid)
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 33C47 | Other special orthogonal polynomials and functions |
| 05E05 | Symmetric functions and generalizations |
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