Admissible majorants for model subspaces, and arguments of inner functions

Author： Baranov A.   Havin V.  

Publisher： Springer Publishing Company

ISSN： 0016-2663

Source： Functional Analysis and Its Applications, Vol.40, Iss.4, 2006-10, pp. : 249-263

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Abstract

Let Θ be an inner function in the upper half-plane + and let K Θ denote the model subspace H 2 ⊖ Θ H 2 of the Hardy space H 2 = H 2(+). A nonnegative function w on the real line is said to be an admissible majorant for K Θ if there exists a nonzero function f ∈ K 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.

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