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Hörmander's Inequality and Point Evaluations in de Branges Space

Bergman, Alex LU orcid (2024)
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
Working paper/Preprint
publication status
published
subject
publisher
arXiv.org
DOI
10.48550/arXiv.2411.02226
language
English
LU publication?
yes
id
c83ce5e8-780f-473f-9a4a-eb4d742d9e14
date added to LUP
2024-11-06 10:42:00
date last changed
2025-04-04 14:33:03
@misc{c83ce5e8-780f-473f-9a4a-eb4d742d9e14,
  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}},
  language     = {{eng}},
  month        = {{11}},
  note         = {{Preprint}},
  publisher    = {{arXiv.org}},
  title        = {{Hörmander's Inequality and Point Evaluations in de Branges Space}},
  url          = {{http://dx.doi.org/10.48550/arXiv.2411.02226}},
  doi          = {{10.48550/arXiv.2411.02226}},
  year         = {{2024}},
}