Transfer-function realization for multipliers of the Arveson space

2006/10/20 by Joseph A. Ball, Ball, Joseph A., Vladimir Bolotnikov +3 · 2 citations
Mathematics · #47A57 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0610637

openalex publication_date 2006/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An interesting and recently much studied generalization of the classical Schur class is the class of contractive operator-valued multipliers for the reproducing kernel Hilbert space \mathcal H(k_d) on the unit ball \mathbb B^d ⊂ \mathbb C^d, where k_d is the positive kernel k_d(λ, ζ) = 1/(1 - < λ, ζ>) on \mathbb B^d. We study this space from the point of view of realization theory and functional models of de Branges-Rovnyak type. We highlight features which depart from the classical univariate case: coisometric realizations have only partial uniqueness properties, the nonuniqueness can be described explicitly, and this description assumes a particularly concrete form in the functional-model context.

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