Decompositions of de Branges-Rovnyak spaces

We obtain orthogonal decompositions for de Branges-Rovnyak spaces \H\left( \tfrac {I^n(1+I)}{2}\right) and \H\left( \tfrac {I(1+I^2)}{2}\right), where $I$ is an inner function. We also discuss the problem of cyclicity for these spaces.