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

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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.