TY - JOUR

T1 - Admissible majorants for model subspaces, and arguments of inner functions

AU - Baranov, A. D.

AU - Havin, V. P.

PY - 2006/10/1

Y1 - 2006/10/1

N2 - Let Θ be an inner function in the upper half-plane ℂ+ and let K Θ denote the model subspace H 2 θ 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 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.

AB - Let Θ be an inner function in the upper half-plane ℂ+ and let K Θ denote the model subspace H 2 θ 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 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.

KW - Beurling-Malliavin theorem

KW - Entire function

KW - Hardy space

KW - Inner function

KW - Model subspace

UR - http://www.scopus.com/inward/record.url?scp=33748548506&partnerID=8YFLogxK

U2 - 10.1007/s10688-006-0042-z

DO - 10.1007/s10688-006-0042-z

M3 - Article

AN - SCOPUS:33748548506

VL - 40

SP - 249

EP - 263

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 4

ER -