In this project the principal investigator will study systematically the zeros of orthogonal Laurent polynomials (L- polynomials) related to strongly positive-definite moment functionals. This study will parallel the study of the zeros of classical orthogonal polynomials. In particular, the principal investigator will look at the separation properties of the zeros and establish the connection between the zeros and the spectrum of a natural representative of the polynomials. She will also study the relationship between the zeros and the true interval of orthogonality of the L-polynomials. The theory of classical orthogonal polynomials is rich in mathematical content and in applications' value to a host of problems in approximation theory, numerical analysis and differential equations. In this the project the principal investigator will attempt to construct an analogous theory for a class of generalized orthogonal polynomials called Laurent polynomials. In particular, she will study the properties of the zeros of such polynomials, in order to broaden the mathematical theory of these objects and to explore exciting applications of Laurent polynomials in approximation theory.//
