## Abstract

In the recent paper by Pakovich and Muzychuk [Solution of the polynomial moment problem, Proc. Lond. Math. Soc. (3) 99 (2009), 633-657] it was shown that any solution of 'the polynomial moment problem', which asks to describe polynomials $Q$ orthogonal to all powers of a given polynomial $P$ on a segment, may be obtained as a sum of so-called 'reducible' solutions related to different decompositions of $P$ into a composition of two polynomials of lower degrees. However, the methods of that paper do not permit us to estimate the number of necessary reducible solutions or to describe them explicitly. In this paper we provide a description of polynomial solutions of the functional equation P_{1} oW_{1} = P_{2} oW_{2} = ... = P_{r} oW_{r}, and on this base describe solutions of the polynomial moment problem in an explicit form suitable for applications.

Original language | English |
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Pages (from-to) | 705-728 |

Number of pages | 24 |

Journal | Compositio Mathematica |

Volume | 149 |

Issue number | 4 |

DOIs | |

State | Published - 1 Apr 2013 |

## Keywords

- center problem
- polynomial decompositions
- polynomial moment problem
- second Ritt theorem