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Factorizations induced by complete Nevanlinna–Pick factors

Aleman, Alexandru LU ; Hartz, Michael ; McCarthy, John E. and Richter, Stefan (2018) In Advances in Mathematics 335. p.372-404
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.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Factorization, Harmonic majorant, Multiplier, Nevanlinna–Pick kernel
in
Advances in Mathematics
volume
335
pages
33 pages
publisher
Academic Press
external identifiers
  • scopus:85049999809
ISSN
0001-8708
DOI
10.1016/j.aim.2018.07.013
language
English
LU publication?
yes
id
afcddf63-d7ad-4479-b6bd-59182bdb0366
date added to LUP
2018-07-31 12:44:44
date last changed
2025-10-14 11:35:14
@article{afcddf63-d7ad-4479-b6bd-59182bdb0366,
  abstract     = {{<p>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|<sup>2</sup> with the property that whenever the majorant is bounded, the corresponding function f is a pointwise multiplier.</p>}},
  author       = {{Aleman, Alexandru and Hartz, Michael and McCarthy, John E. and Richter, Stefan}},
  issn         = {{0001-8708}},
  keywords     = {{Factorization; Harmonic majorant; Multiplier; Nevanlinna–Pick kernel}},
  language     = {{eng}},
  month        = {{09}},
  pages        = {{372--404}},
  publisher    = {{Academic Press}},
  series       = {{Advances in Mathematics}},
  title        = {{Factorizations induced by complete Nevanlinna–Pick factors}},
  url          = {{http://dx.doi.org/10.1016/j.aim.2018.07.013}},
  doi          = {{10.1016/j.aim.2018.07.013}},
  volume       = {{335}},
  year         = {{2018}},
}