Schur Multipliers and de Branges Rovnyak Spaces: The Multiscale Case

Document Type


Publication Date



We consider bounded linear operators acting on the ℓ2 space indexed by the nodes of a homogeneous tree. Using the Cuntz relations between the primitive shifts on the tree, we generalize the notion of the single-scale time-varying point evaluation and introduce the corresponding reproducing kernel Hilbert space in which Cauchy’s formula holds. These notions are then used in the study of the Schur multipliers and of the associated de Branges – Rovnyak spaces. As an application we obtain realization of Schur multipliers as transfer operators of multiscale input-state-output systems.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Operator Theory, volume 61, in 2009 following peer review. This article may not exactly replicate the final published version.

Peer Reviewed



American Mathematical Society