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

Part of: Qualitative theory Curves Miscellaneous topics of analysis in the complex domain

Published online by Cambridge University Press:  29 January 2013

F. Pakovich
F. Pakovich*
Affiliation:
Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva, Israel (email: pakovich@math.bgu.ac.il)
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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 $P_1\circ W_1=P_2\circ W_2=\cdots =P_r\circ W_r,$and on this base describe solutions of the polynomial moment problem in an explicit form suitable for applications.

Keywords

polynomial moment problemsecond Ritt theorempolynomial decompositionscenter problem

MSC classification

Secondary: 30E99: None of the above, but in this section 14H30: Coverings, fundamental group 34C99: None of the above, but in this section

Information

Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 4 , April 2013 , pp. 705 - 728
Copyright
Copyright © 2013 The Author(s)

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