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Hörmander’s inequality and point evaluations in de Branges space

Bergman, Alex LU orcid (2026) In Revista Matematica Iberoamericana 42(2). p.551-572
Abstract

Let f be an entire function of finite exponential type less than or equal to σwhich is bounded by 1 on the real axis and satisfies f(0)=1. Under these assumptions, Hörmander showed that f cannot decay faster than cos(σx) on the interval (-π/σ,π/σ). We extend this result to the setting of de Branges spaces with cosine replaced by the real part of the associated Hermite–Biehler function. We apply this result to study the point evaluation functional and associated extremal functions in de Branges spaces (equivalently, in model spaces generated by meromorphic inner functions), generalizing some recent results of Brevig, Chirre, Ortega-Cerdà, and Seip.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
de Branges space, entire functions, extremal inequality
in
Revista Matematica Iberoamericana
volume
42
issue
2
pages
22 pages
publisher
EMS Publishing House
external identifiers
  • scopus:105031506850
ISSN
0213-2230
DOI
10.4171/RMI/1582
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2026 Real Sociedad Matemática Española. Published by EMS Press and licensed under a CC BY 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
id
f7f93b40-fb77-43d4-91a6-45d67daac0c2
date added to LUP
2026-04-13 15:45:05
date last changed
2026-05-11 19:16:33
@article{f7f93b40-fb77-43d4-91a6-45d67daac0c2,
  abstract     = {{<p>Let f be an entire function of finite exponential type less than or equal to σwhich is bounded by 1 on the real axis and satisfies f(0)=1. Under these assumptions, Hörmander showed that f cannot decay faster than cos(σx) on the interval (-π/σ,π/σ). We extend this result to the setting of de Branges spaces with cosine replaced by the real part of the associated Hermite–Biehler function. We apply this result to study the point evaluation functional and associated extremal functions in de Branges spaces (equivalently, in model spaces generated by meromorphic inner functions), generalizing some recent results of Brevig, Chirre, Ortega-Cerdà, and Seip.</p>}},
  author       = {{Bergman, Alex}},
  issn         = {{0213-2230}},
  keywords     = {{de Branges space; entire functions; extremal inequality}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{551--572}},
  publisher    = {{EMS Publishing House}},
  series       = {{Revista Matematica Iberoamericana}},
  title        = {{Hörmander’s inequality and point evaluations in de Branges space}},
  url          = {{http://dx.doi.org/10.4171/RMI/1582}},
  doi          = {{10.4171/RMI/1582}},
  volume       = {{42}},
  year         = {{2026}},
}