Mathematical Sciences: Potential Theoretical Methods in Approximation Theory

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In this project the principal investigator will continue his research on the asymptotic behavior of orthogonal polynomials and their zeros with respect to general weights with compact support in the plane. He will also explore the possibility of using potential theory to study orthogonal polynomials in collaboration with faculty members at the University of South Florida. Finally the principal investigator will study asymptotic questions related to the support of the Christoffel function under fairly general assumptions. The study of the properties of orthogonal polynomials is important in its own right and for the light it sheds on various problems in approximation theory, numerical analysis and differential equations. In this project the principal investigator, in collaboration with experts at the University of South Florida, will continue his valuable work on the asymptotic properties of orthogonal polynomials under general conditions through the use of potential theory.