On the problem of smooth approximations in H(b) and connections to subnormal operators
For the class of de Branges-Rovnyak spaces H(b) of the unit disk D defined by extreme points b of the unit ball of H∞, we study the problem of approximation of a general function in H(b) by a function with an extension to the unit circle T of some degree of smoothness, for instance satisfying Hölder estimates or being differentiable. We will exhibit connections between this question and the theory