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Functional Analysis and Its Applications

, Volume 40, Issue 4, pp 249–263 | Cite as

Admissible majorants for model subspaces, and arguments of inner functions

  • A. D. Baranov
  • V. P. Havin
Open Access
Article

Abstract

Let Θ be an inner function in the upper half-plane ℂ+ and let K Θ denote the model subspace H 2 ⊖ Θ H 2 of the Hardy space H 2 = H 2(ℂ+). A nonnegative function w on the real line is said to be an admissible majorant for K Θ if there exists a nonzero function fK Θ such that {f} ⩽ w a.e. on ℝ. We prove a refined version of the parametrization formula for K Θ-admissible majorants and simplify the admissibility criterion (in terms of arg Θ) obtained in [8]. We show that, for every inner function Θ, there exist minimal K Θ-admissible majorants. The relationship between admissibility and some weighted approximation problems is considered.

Key words

Hardy space inner function model subspace entire function Beurling-Malliavin theorem 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. D. Baranov
    • 1
  • V. P. Havin
    • 1
  1. 1.S.-Petersburg State UniversityRussia

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