Laurent polynomial moment problem: a case study

TL;DR

This paper explores the Laurent polynomial moment problem, demonstrating that solutions can exhibit more complex behavior than polynomial cases, thus advancing understanding in rational function moment problems.

Contribution

It constructs an example of a Laurent polynomial with notably complex solution behavior, extending the polynomial moment problem to rational functions.

Findings

Constructed a Laurent polynomial with complex solution behavior

Showed differences between polynomial and Laurent polynomial moment problems

Progressed understanding of rational function moment problems

Abstract

In recent years, the so-called polynomial moment problem, motivated by the classical Poincare center-focus problem, was thoroughly studied, and the answers to the main questions have been found. The study of a similar problem for rational functions is still at its very beginning. In this paper, we make certain progress in this direction; namely, we construct an example of a Laurent polynomial for which the solutions of the corresponding moment problem behave in a significantly more complicated way than it would be possible for a polynomial.