Representation formulas for Hardy space functions through the Cuntz   relations and new interpolation problems
  We introduce connections between the Cuntz relations and the Hardy space H_2 of the open unit disk . We then use them to solve a new kind of multipoint interpolation problem in H_2, where for instance, only a linear combination of the values of a function at given points is preassigned, rather than the values at the points themselves. We also consider the case of de Branges-Rovnyak spaces. 
Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz, Itzik Martziano
math.FA