Geodesic
Model functions with nearly prescribed modulus
Algebra i analiz, Tome 20 (2008) no. 2, pp. 3-18.

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Let $\Theta$ be an inner function on the upper half-plane, and let $K_\Theta=H^2\ominus\Theta H^2 $ be the corresponding model subspace. A nonnegative measurable function $\omega$ is said to be strongly admissible for $K_{\Theta}$ if there exists a nonzero function $f\in K_{\Theta}$ with $|f|\asymp\omega$. Certain condition sufficient for strong admissibility are given in the case where $\Theta$ is meromorphic.
Keywords: Admissible function, Beurling–Mallivin theorem, model subspace, logarithmic integral. 
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Yu. S. Belov. Model functions with nearly prescribed modulus. Algebra i analiz, Tome 20 (2008) no. 2, pp. 3-18. http://geodesic.mathdoc.fr/item/AA_2008_20_2_a0/

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