Approximating Positive Polynomials Using Sums of Squares

http://dx.doi.org/10.4153/CMB-2003-041-9
Canad. Math. Bull. 46(2003), 400-418

  Published:2003-09-01
 Printed: Sep 2003

The paper considers the relationship between positive polynomials, sums of squares and the multi-dimensional moment problem in the general context of basic closed semi-algebraic sets in real $n$-space. The emphasis is on the non-compact case and on quadratic module representations as opposed to quadratic preordering presentations. The paper clarifies the relationship between known results on the algebraic side and on the functional-analytic side and extends these results in a variety of ways.