Composition operator on de Branges-Rovnyak spaces

Abstract

If α which is analytic and which maps the unit disc to itself. Then we describe the image of the de Branges-Rovnyak spaces H(b) under the composition operator Cα for algebraic functions b. In this thesis, we answered partially about what are the conditions on α such that Cα maps H(b) into itself, which are α’s such that Cα : H(b) −→ H(b), and which are α’s such that Cα maps H(b) to H(q).