Generalized 'second Ritt theorem' and explicit solution of the polynomial moment problem

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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 P1 oW1 = P2 oW2 = ... = Pr oWr, and on this base describe solutions of the polynomial moment problem in an explicit form suitable for applications.

Original languageEnglish
Pages (from-to)705-728
Number of pages24
JournalCompositio Mathematica
Volume149
Issue number4
DOIs
StatePublished - 1 Apr 2013

Keywords

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

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