Solution of the polynomial moment problem

By F. Pakovich, Mikhail E. Muzychuk. 2007

64 citations recorded by the source corpus.

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].

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/850e5a0aa5d8590fbcfec5eb2ab0e2b35b78490d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. M. Briskin
2. N. Roytvarf
3. Colin Christopher
4. Y. Yomdin
5. A. Álvarez
6. Wenhua Zhao
7. J. Bravo

In Geometry and Topology

1. M. Briskin
2. N. Roytvarf
3. Colin Christopher
4. Y. Yomdin
5. A. Álvarez
6. Wenhua Zhao
7. J. Bravo
8. F. Pakovich

Citations in the corpus

• On the trigonometric moment problem (2011, background): “Recently it has been completely solved by Muzychuk and Pakovich [17] who show that Q satisfies (1.”
• Center conditions at infinity for Abel differential equations (2010, methodology): “Still, a complete answer has been obtained only very recently ([53]).”
• Mathieu Subspaces of Associative Algebras (2010, background): “ series of papers [BFY1]-[BFY5], which was mainly motivated by the center problem for the complex Abel equation. For some recent studies on the polynomial moment problem in one or more variables, see [PM], [Pa], [Z4] and [FPYZ]. Currently, it is also under investigations by the author and some of hi”