Modifications of the Schwarz lemma for regular functions on a free domain

Anastasia Frolova, a new Master's student in the Analysis group will tell about the work she carried out in the process of writing her Bachelor's thesis.

Title: "Modifications of the Schwarz lemma for regular functions on a free domain"

Abstract: We consider regular functions defined on an arbitrary open subset of the unit disk containing zero. Using classical properties of conformal maps and a sufficient condition for univalence for such functions we get special modifications of the Schwarz lemma and inequalities for the functions’ coefficients. In particular, we apply such estimates to algebraic polynomials.