Factorizations induced by complete Nevanlinna–Pick factors
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/afcddf63-d7ad-4479-b6bd-59182bdb0366
- author
- Aleman, Alexandru LU ; Hartz, Michael ; McCarthy, John E. and Richter, Stefan
- organization
- publishing date
- 2018-09-07
- 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
- Elsevier
- 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
- 2022-03-09 19:50:53
@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 = {{Elsevier}}, 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}}, }