Mathematical Sciences: Potential Theoretical Methods in Approximation Theory

在这个项目中，主要研究者将继续研究平面上紧支集的正交多项式及其零点关于一般权值的渐近行为。他还将与南佛罗里达大学的教职员工合作，探索利用位势理论研究正交多项式的可能性。最后，主要研究者将在相当普遍的假设下研究与Christoffel函数的支撑性有关的渐近问题。研究正交多项式的性质本身就很重要，因为它揭示了逼近理论、数值分析和微分方程式中的各种问题。在这个项目中，首席研究员将与南佛罗里达大学的专家合作，通过使用位势理论继续他在一般条件下关于正交多项式的渐近性质的有价值的工作。

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.