Solution of the polynomial moment problem

F. Pakovich; M. Muzychuk

doi:10.1112/plms/pdp010

Solution of the polynomial moment problem

F. Pakovich, M. Muzychuk

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

In this paper we give a solution of the following 'polynomial moment problem' which arose about 10 years ago in connection with Poincaré's center-focus problem: for a given polynomial P(z) to describe polynomials q(z) orthogonal to all powers of P(z) on a segment [a, b].

Original language	English
Pages (from-to)	633-657
Number of pages	25
Journal	Proceedings of the London Mathematical Society
Volume	99
Issue number	3
DOIs	https://doi.org/10.1112/plms/pdp010
State	Published - 1 Nov 2009

ASJC Scopus subject areas

General Mathematics

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title = "Solution of the polynomial moment problem",

abstract = "In this paper we give a solution of the following 'polynomial moment problem' which arose about 10 years ago in connection with Poincar{\'e}'s center-focus problem: for a given polynomial P(z) to describe polynomials q(z) orthogonal to all powers of P(z) on a segment [a, b].",

author = "F. Pakovich and M. Muzychuk",

note = "Funding Information: Received 24 October 2007; revised 4 February 2009; published online 31 March 2009. 2000 Mathematics Subject Classification 30E99 (primary), 34C99, 20C05, 12F10 (secondary). The research of the first author was supported by the ISF grant no. 979/07.",

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N2 - In this paper we give a solution of the following 'polynomial moment problem' which arose about 10 years ago in connection with Poincaré's center-focus problem: for a given polynomial P(z) to describe polynomials q(z) orthogonal to all powers of P(z) on a segment [a, b].

AB - In this paper we give a solution of the following 'polynomial moment problem' which arose about 10 years ago in connection with Poincaré's center-focus problem: for a given polynomial P(z) to describe polynomials q(z) orthogonal to all powers of P(z) on a segment [a, b].

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Solution of the polynomial moment problem

Abstract

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