On nonglobal positivity and domains of positivity of multivariable polynomials

In this paper, a test for the nonglobal positivity of multivariable polynomials over specified real intervals of the independent variables is discussed and the results are illustrated by a nontrivial example. The problem of determining the domains of positivity of a multivariable polynomial is then considered and the details of the procedure are illustrated by a nontrivial two-variable example. Computational aspects in the implementation of the method are mentioned and wide scopes for application of the results in various problems of system theory are pointed out.