Geodesic
Admissibility criteria for model subspaces with fast growth of the argument of the generating inner function
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 35, Tome 345 (2007), pp. 55-84 
Yu. S. Belov. Admissibility criteria for model subspaces with fast growth of the argument of the generating inner function. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 35, Tome 345 (2007), pp. 55-84. http://geodesic.mathdoc.fr/item/ZNSL_2007_345_a3/
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     title = {Admissibility criteria for model subspaces with fast growth of the argument of the generating inner function},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_345_a3/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $\Theta$ be an inner function in the upper half plane and let $K_\Theta=H^2\ominus\Theta H^2$ be the associated model subspace of the Hardy space $H^2$. We call a non-negative function $\omega$ $\Theta$-admissible if in the space $K_\Theta$ there exists a non-zero function $f\in K_\Theta$ such that $|f|\leq\omega$ a.e. on $\mathbb{R}$. We give some sufficient conditions of $\Theta$-admissibility for the case when $\Theta$ is meromorphic and $\arg\Theta$ grows fast ($(\arg\Theta)'$ tends to infinity).

[1] A. D. Baranov, “Polynomials in the de Branges spaces of entire functions”, Ark. Mat., 44:1 (2006), 16–38 | DOI | MR | Zbl

[2] Yu. S. Belov, “Neobkhodimye usloviya dopustimosti dlya nekotorykh klassov modelnykh podprostranstv” (to appear)

[3] A. D. Baranov, V. P. Khavin, “Dopustimye mazhoranty dlya modelnykh podprostranstv i argumenty vnutrennikh funktsii”, Funktsionalnyi analiz i ego prilozheniya, 40:4 (2006), 2–21 | MR

[4] A. D. Baranov, A. A. Borichev, V. P. Havin, “Admissible majorants for meromorphic functions with fixed poles”, Indiana University Math. J. (to appear)

[5] V. Havin, B. Jöricke, The Uncertainty Principle in Harmonic Analysis, Springer-Verlag, 1994 | MR

[6] V. P. Havin, J. Mashreghi, “Admissible majorants for model subspaces of $H^2$. Part 1: slow winding of the generating inner function”, Can. J. Math., 55:6 (2003), 1231–1263 | DOI | MR | Zbl

[7] V. P. Havin, J. Mashreghi, “Admissible majorants for model subspaces of $H^2$. Part 2: fast winding of the generating inner function”, Can. J. Math., 55:6 (2003), 1264–1301 | DOI | MR | Zbl

[8] P. Koosis, The Logarithmic integral, I, Cambridge Stud. Adv. Math., 12, Cambridge University Press, Cambridge, 1988 | MR | Zbl

[9] V. P. Khavin, Dzh. Mashregi, F. Nazarov, “Teorema Berlinga–Malyavena o multiplikatore: sedmoe dokazatelstvo”, Algebra i Analiz, 17:5 (2005), 3–68 | MR