Resumen de On the relation between Darboux transformations and polynomial mappings

Maxim S. Derevyagin

• 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.