Mini-course on de Branges-Rovnyak Spaces - Part 1

Explore the foundations of de Branges-Rovnyak spaces in this comprehensive lecture from the Focus Program on Analytic Function Spaces and their Applications. Delve into key concepts including notation, historical context, multipliers, and Bronzerovnik spaces. Examine range spaces, general lemmas, and various types of Rovnyak spaces. Investigate the Douglas lemma and its proof, along with antifunctions and boundary behavior. Gain valuable insights from Dan Timotin of the Simion Stoilow Institute of Mathematics as he presents this in-depth exploration of complex analysis and functional theory.

Introduction
Notation
History
Multipliers
Bronzerovnik Spaces
Range Spaces
General Lemma
Types of Rovnyak Spaces
Douglaslemma
Proof
Antifunctions
Behavior of the boundary