Interpolation in multivariable de Branges-Rovnyak spaces

TL;DR

This paper investigates a broad class of interpolation problems within de Branges-Rovnyak spaces linked to contractive multipliers, extending classical results to multivariable and operator-valued settings.

Contribution

It introduces a unified approach to interpolation in multivariable de Branges-Rovnyak spaces associated with Fock and Drury-Arveson spaces, generalizing existing single-variable theories.

Findings

Established new interpolation criteria in multivariable de Branges-Rovnyak spaces.

Connected interpolation problems in Fock spaces with those in the Drury-Arveson space.

Provided a framework for analyzing contractive multipliers in multivariable contexts.

Abstract

We study a general metric constrained interpolation problem in a de Branges-Rovnyak space $\mathcal{H}(K_S)$ associated with a contractive multiplier $S$ between two Fock spaces along with its commutative counterpart, a de Branges-Rovnyak space associated with a Schur multiplier on the Drury-Arveson space of the unit ball of $\mathbb{C}^n$.