# On the problem of smooth approximations in de Branges-Rovnyak spaces and connections to subnormal operators

@inproceedings{Limani2021OnTP, title={On the problem of smooth approximations in de Branges-Rovnyak spaces and connections to subnormal operators}, author={Adem Limani and Bartosz Malman}, year={2021} }

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 of subnormal operators and, in particular, we will tie the possibility of smooth approximations to…

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