A multiplier algebra functional calculus

This paper generalizes the classical Sz.-Nagy–Foias $H^{\mathrm{\infty }}(\mathbb{D})$ functional calculus for Hilbert space contractions. In particular, we replace the single contraction $T$ with a tuple $T=(T_1,\dots ,T_d)$ of commuting bounded operators on a Hilbert space and replace $H^{\mathrm{\infty }}(\mathbb{D})$ with a large class of multiplier algebras of Hilbert function spaces on the unit ball in ${\mathbb{C}}^d$.