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- W2096246872 abstract "In the recent paper arXiv:0710.4085 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 some reducible solutions related to different decompositions of P into a composition of two polynomials of lesser degrees. However, the methods of arXiv:0710.4085 do not permit to estimate the number of necessary reducible solutions or to describe them explicitly. In this paper we provide a description of the polynomial solutions of the functional equation P=P_1(W_1)=P_2(W_2)=...=P_r(W_r), and on this base describe solutions of the polynomial moment problem in an explicit form suitable for applications. With respect to the previous version a more general form of the generalized secon Ritt theorem is proved and the proof is considerably simplified. Besides, a missed case in Theorem 1.2 was added and the proof is corrected." @default.
- W2096246872 created "2016-06-24" @default.
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- W2096246872 date "2009-08-18" @default.
- W2096246872 modified "2023-10-18" @default.
- W2096246872 title "Generalized second Ritt theorem and explicit solution of the polynomial moment problem" @default.
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- W2096246872 doi "https://doi.org/10.48550/arxiv.0908.2508" @default.
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