# Generalized second Ritt theorem and explicit solution of the polynomial moment problem - Mathematics > Dynamical Systems

Generalized second Ritt theorem and explicit solution of the polynomial moment problem - Mathematics > Dynamical Systems - Download this document for free, or read online. Document in PDF available to download.

Abstract: In the recent paper arXiv:0710.4085 was shown that any solution of -thepolynomial moment problem-, which asks to describe polynomials Q orthogonal toall powers of a given polynomial P on a segment, may be obtained as a sum ofsome -reducible- solutions related to different decompositions of P into acomposition of two polynomials of lesser degrees. However, the methods ofarXiv:0710.4085 do not permit to estimate the number of necessary reduciblesolutions or to describe them explicitly. In this paper we provide adescription of the polynomial solutions of the functional equationP=P 1W 1=P 2W 2=

.=P rW r, and on this base describe solutions of thepolynomial moment problem in an explicit form suitable for applications. Withrespect to the previous version a more general form of the generalized -seconRitt theorem- is proved and the proof is considerably simplified. Besides, amissed case in Theorem 1.2 was added and the proof is corrected.

Author: ** F. Pakovich**

Source: https://arxiv.org/