Factorizations induced by complete Nevanlinna-Pick factors

Abstract

We prove a factorization theorem for reproducing kernel Hilbert spaces whose kernel has a normalized complete Nevanlinna-Pick factor. This result relates the functions in the original space to pointwise multipliers determined by the Nevanlinna-Pick kernel and has a number of interesting applications. For example, for a large class of spaces including Dirichlet and Drury-Arveson spaces, we construct for every function $f$ in the space a pluriharmonic majorant of $|f{|}^2$ with the property that whenever the majorant is bounded, the corresponding function $f$ is a pointwise multiplier.

35 pages; minor changes

References in corpus (2)

• Multiplier algebras of complete Nevanlinna-Pick spaces: dilations, boundary representations and hyperrigidity
• The Smirnov class for spaces with the complete Pick property

Cited by in corpus (3)

• A Beurling-Lax-Halmos theorem for spaces with a complete Nevanlinna-Pick factor
• Totally null sets and capacity in Dirichlet type spaces
• Sub-Bergman Hilbert spaces on the unit disk III