Abstract: In the recent series of papers of M. Briskin, J.-P. Francoise and Y. Yomdin, the following "polynomial moment problem" was proposed as an infinitesimal version of the center problem for the Abel differential equation in the complex domain:

For a complex polynomial P(z) and distinct complex numbers a and b such that P(a)=P(b), describe polynomials q(z) orthogonal to all powers of P(z) on the segments [a,b].