Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Inner approximations of doubling weights with applications to Beurling-Malliavin theory in Toeplitz kernels

Bergman, Alex LU orcid (2025)
Abstract
Let f be a strictly increasing smooth function, such that f′ is comparable to a weight α′ which is locally doubling and satisfies a non-triviality condition to be explained in the paper. We construct a meromorphic inner function J, such that f−arg(J) is bounded and arg(J)′ is comparable to α′ up to polynomial loss. We give two applications of this result. The first is a sufficient density condition for a set Λ to be a zero set for a Toeplitz kernel with real analytic and unimodular symbol. Our second application is to describe a class of admissible Beurling-Malliavin majorants in model spaces. The generality considered here lets us treat most cases of model spaces generated by one-component inner functions.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Working paper/Preprint
publication status
published
subject
pages
20 pages
publisher
arXiv.org
language
English
LU publication?
yes
id
05700665-b1dd-4955-82b2-3a3a44c08069
alternative location
https://arxiv.org/abs/2509.21229
date added to LUP
2025-12-09 09:02:17
date last changed
2025-12-18 17:44:24
@misc{05700665-b1dd-4955-82b2-3a3a44c08069,
  abstract     = {{Let f be a strictly increasing smooth function, such that f′ is comparable to a weight α′ which is locally doubling and satisfies a non-triviality condition to be explained in the paper. We construct a meromorphic inner function J, such that f−arg(J) is bounded and arg(J)′ is comparable to α′ up to polynomial loss. We give two applications of this result. The first is a sufficient density condition for a set Λ to be a zero set for a Toeplitz kernel with real analytic and unimodular symbol. Our second application is to describe a class of admissible Beurling-Malliavin majorants in model spaces. The generality considered here lets us treat most cases of model spaces generated by one-component inner functions.}},
  author       = {{Bergman, Alex}},
  language     = {{eng}},
  month        = {{09}},
  note         = {{Preprint}},
  publisher    = {{arXiv.org}},
  title        = {{Inner approximations of doubling weights with applications to Beurling-Malliavin theory in Toeplitz kernels}},
  url          = {{https://arxiv.org/abs/2509.21229}},
  year         = {{2025}},
}