Balschke Products and Their Critical Values

Sammanfattning: This paper concerns the problem of defining and computing a Blaschke product from a prescribed set of critical values. First a mathematical and theoretical background to Blaschke products and their critical values is presented, e.g. the Blaschke condition, important characteristics of finite Blaschke products and the uniqueness theorem. The problem is then presented and the paper walks through a computational method using gaussian curvature. In the same chapter the problem is then compared to some equivalent questions. Lastly two discrete methods are presented and compared. The first method uses the theory of circle packing as presented by Ken Stephenson and the second uses numerical methods to rewrite the problem as a quadratic matrix of linear equations.