Polynomials non-negative on strips and half-strips

Abstract: In 2008, Marshall (2010) settled a long-standing open problem by showing that if is a polynomial that is non-negative on the strip , then there exist sums of squares such that . In this paper, we generalize Marshall’s result to various strips and half-strips in the plane. Our results give many new examples of non-compact semialgebraic sets in for which one can characterize all polynomials which are non-negative on the set. For example, we show that if is a compact subset of the real line and a specific set of generators for as a semialgebraic set, then whenever is non-negative on , there are sums of squares such that . [Copyright &y& Elsevier]