Commutant Lifting and Nevanlinna–Pick Interpolation in Several Variables

Abstract

This paper concerns a commutant lifting theorem and a Nevanlinna–Pick type interpolation result in the setting of multipliers from vector-valued Drury–Arveson space to a large class of vector-valued reproducing kernel Hilbert spaces over the unit ball in Cⁿ. The special case of reproducing kernel Hilbert spaces includes all natural examples of Hilbert spaces like Hardy space, Bergman space and weighted Bergman spaces over the unit ball.