Abstract:

We give two new characterizations of pairs of polynomials or trigonometric polynomials that form a composition pair. In particular one of them proves that the vanishing of a given number of double moments implies that they form a composition pair. This number only depends on the maximum degree of both polynomials. This is the first time that composition is characterized in terms of the vanishing of an explicit number of double moments. Our results allow to recognize the composition centers for polynomial and trigonometric Abel differential equations.

This talk is based on a joint work with Anna Cima and Armengol Gasull.