After successful completion of the course, students are able to overview the theory of orthogonal polynomials and apply methods from operator theory and complex analysis within this theory. 

In the lecture different aspects of the theory of orthogonal polynomials associated to real masses will be treated. Starting from classical problems, such as the existence and uniqueness of the solution of the moment problem, we will deal with spectral theoretical problems of so-called Jacobi operators. Students will learn the basics of how to use cmethods form complex analysis and operator theory to obtain spectral results for this class of operators.

orthogonal polynomials

moment problem

Jacobi operators

Weyl m-function

direct spectral theory of periodic Jacobi operators  

The lecture will be given as a blackboard lecture.

Der erste Termin der Vorlesung ist Dienstag 03.10. im Raum DA 06 G14 (alte Institutsbibliothek gruener Bereich 6. Stock). Weitere Termin nach Absprache mit den Studierenden.

The evaluation of the student will be by an oral exam.