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Representation formulas for Hardy space functions through the Cuntz relations and new interpolation problems

By Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz and Itzik Martziano

Abstract

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.Comment: Updated bibliography and one section added on the case of de Branges Rovnyak space

Topics: Mathematics - Functional Analysis, 42C40, 47A57, 93B28
Year: 2011
OAI identifier: oai:arXiv.org:1104.0621
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