On the relation between Darboux transformations and polynomial mappings
- Autores: Maxim S. Derevyagin
- Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 172, Nº 1, 2013, págs. 4-22
- Idioma: inglés
- DOI: 10.1016/j.jat.2013.04.002
- Enlaces
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Resumen
Let d£g be a probability measure on [0,+¡Û) such that its moments are finite. Then the Cauchy¡VStieltjes transform S of d£g is a Stieltjes function, which admits an expansion into a Stieltjes continued fraction. In the present paper, we consider a matrix interpretation of the unwrapping transformation S(£f) �Ö¡÷ £fS(£f2), which is intimately related to the simplest case of polynomial mappings. More precisely, it is shown that this transformation is essentially a Darboux transformation of the underlying Jacobi matrix. Moreover, in this scheme, the Chihara construction of solutions to the Carlitz problem appears as a shifted Darboux transformation.
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