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Hörmander's inequality and point evaluations in de Branges space

Bergman, Alex LU orcid (2025) In Revista Matemática Iberoamericana 2025.
Abstract
Let f be an entire function of finite exponential type less than or equal to σ which 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
in
Revista Matemática Iberoamericana
volume
2025
pages
22 pages
publisher
EMS Publishing House
ISSN
2235-0616
language
English
LU publication?
yes
id
4fbeca6d-2c61-44ee-b1d7-d9aa197a9791
alternative location
https://ems.press/journals/rmi/articles/14298986
date added to LUP
2025-12-09 08:59:25
date last changed
2025-12-18 17:35:40
@article{4fbeca6d-2c61-44ee-b1d7-d9aa197a9791,
  abstract     = {{Let f be an entire function of finite exponential type less than or equal to σ which 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.}},
  author       = {{Bergman, Alex}},
  issn         = {{2235-0616}},
  language     = {{eng}},
  month        = {{07}},
  publisher    = {{EMS Publishing House}},
  series       = {{Revista Matemática Iberoamericana}},
  title        = {{Hörmander's inequality and point evaluations in de Branges space}},
  url          = {{https://ems.press/journals/rmi/articles/14298986}},
  volume       = {{2025}},
  year         = {{2025}},
}