Factorizations induced by complete Nevanlinna–Pick factors

Research output: Contribution to journalArticle

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.

Details

Authors
Organisations
External organisations
  • Washington University in St. Louis
  • University of Tennessee
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • Factorization, Harmonic majorant, Multiplier, Nevanlinna–Pick kernel
Original languageEnglish
Pages (from-to)372-404
Number of pages33
JournalAdvances in Mathematics
Volume335
StatePublished - 2018 Sep 7
Publication categoryResearch
Peer-reviewedYes