We introduce connections between the Cuntz relations and the Hardy space H2 of the open unit disk D. We then use them to solve a new kind of multipoint interpolation problem in H2, 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.
D. Alpay, P. Jorgensen, I. Lewkowicz and I. Marziano. Representation formulas for Hardy space functions through the Cuntz relations and new interpolation problems. Multiscale signal analysis and modeling (editors Xiaoping Shen and Ahmed Zayed), Lecture Notes in Electrical Engineering (Springer), (2013), pp. 161-182.