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Proceedings of the London Mathematical Society Advance Access originally published online on March 31, 2009
Proceedings of the London Mathematical Society 2009 99(3):633-657; doi:10.1112/plms/pdp010
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© 2009 London Mathematical Society

Solution of the polynomial moment problem

F. Pakovich

Department of Mathematics
Ben Gurion University
POB 653
Beer Sheva 84105
Israel

M. Muzychuk

Department of Mathematics
Netanya Academic College
Kibbutz Galuyot St. 16
Netanya 42365
Israel
muzy@netanya.ac.il

Received 24 October 2007. Revision received 4 February 2009.

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].

The research of the first author was supported by the ISF grant no. 979/07.

2000 Mathematics Subject Classification 30E99 (primary), 34C99, 20C05, 12F10 (secondary).


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