Factorial-type Schur functions, orthogonal rational functions, and discrete dressing chains (Q2814218)
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scientific article; zbMATH DE number 6595460
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Factorial-type Schur functions, orthogonal rational functions, and discrete dressing chains |
scientific article; zbMATH DE number 6595460 |
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Factorial-type Schur functions, orthogonal rational functions, and discrete dressing chains (English)
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20 June 2016
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factorial-type Schur function
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orthogonal rational function
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discrete dressing chain
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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.
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