2006/05/12 by Daniel Alpay, Aad Dijksma, Alpay, Daniel +3 · 1 citation
Mathematics · #05C05 #93B28 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #math.FA #math.OA #msc:05C05 #msc:93B28
paper · pdf · doi:10.48550/arxiv.math/0605331
final version
openalex publication_date 2006/05/12 · arxiv created 2007/03/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.