NSCPHD1211 The Moment Problem and Orthogonal Polynomials

Knowledge:

After the course the students should know weak and vague convergence of measures on Euclidean spaces and the relation to convergence of the corresponding moments. They should know how different moment sequences can be characterized in terms of positive definiteness. They should know the basics about orthogonal polynomials such as the three term recurrence relation and interlacing of zeros. They should learn that a moment problem can be determinate or indeterminate and how to distinguish the two cases.

Skills:

The students should be able to calculate moments of concrete measures,
master the formulas defining some of the classical systems of orthogonal polynomials, be able to decide vague or weak convergence of concrete sequences of measures, apply the given criteria to decide the nature of the moment problem. 

Competences:

The students should get insight in a classical subject, which has been important in the development of mathematics of the 20'th century. The students should get a deeper understanding of linear algebra, measure theory and real and complex analysis, which are the three subjects which are vital in the course.