Science in Developing Countries: Orthogonal Polynomials, Differential Equations, and Difference Equations

该奖项将支持坦帕南佛罗里达大学的Mourad Ismail教授和哥伦比亚波哥大哥伦比亚国立大学的Jairo Charris教授之间的合作研究。研究人员计划在以下三个方面开展研究：1)微分方程，2)差分方程，3)正交多项式。更具体地说，他们计划研究一类具有任意数量的正则奇点的二阶微分方程。他们还计划构造某些四阶差分方程族的谱测度，并研究由具有拟周期势的离散薛定谔算子产生的正交多项式。此外，他们还将研究几个区间上的正交多项式，以及依赖于参数的正交多项式的零点的分布和单调性。这位美国研究员是一位经验丰富、受人尊敬的研究员，在这些领域取得了重要成果。通过帮助伊斯梅尔教授和一位来自发展中国家的有前途的研究人员共同研究共同感兴趣的问题，该奖项实现了发展中国家科学计划的目标。

This award will support collaborative research between Professor Mourad Ismail of the University of South Florida in Tampa and Professor Jairo Charris of the National University of Colombia in Bogota, Colombia. The investigators plan to carry out research problems in the following three areas: 1) Differential Equations, 2) Difference Equations, and 3) Orthogonal Polynomials. More specifically, they plan to study a class of differential equations of order 2 with an arbitrary number of regular singular points. They also plan to construct spectral measures of certain families of fourth order difference equations and study orthogonal polynomials arising from discrete Schrodinger operators with quasi periodic potentials. Additionally, they will investigate polynomials orthogonal on several intervals and the distribution and monotonicity of zeros of orthogonal polynomials depending on a parameter. The U.S. investigator is an experienced and respected researcher who has obtained important results in these areas. By helping to bring together Professor Ismail with a promising researcher from a developing country to work on problems of mutual interest, this award fulfills the objectives of the Science in Developing Countries Program.