Geodesic
Admissibility of majorants in certain model subspaces: necessary conditions
Algebra i analiz, Tome 20 (2008) no. 4, pp. 1-26.

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A nonnegative function $\omega$ on $\mathbb{R}$ is called an admissible majorant for an inner function $\Theta$ if there is a nonzero function $f\in H^2\ominus\Theta H^2$ such that $|f|\le\omega$. Some conditions necessary for admissibility are presented in the case where $\Theta$ is meromorphic.
Keywords: Blaschke product, model subspace, admissible majorant, Beurling–Malliavin theorem. 
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Yu. S. Belov. Admissibility of majorants in certain model subspaces: necessary conditions. Algebra i analiz, Tome 20 (2008) no. 4, pp. 1-26. http://geodesic.mathdoc.fr/item/AA_2008_20_4_a0/

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

[Ba] Bari N. K., Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR

[BB] Baranov A. D., Borichev A. A., Entire functions of exponential type with prescribed modulus on the real axis, ne opublikovano

[BBH] Baranov A. D., Borichev A. A., Havin V. P., “Majorants of meromorphic functions with fixed poles”, Indiana Univ. Math. J., 56:4 (2007), 1595–1628 | DOI | MR | Zbl

[BH] Baranov A. D., Khavin V. P., “Dopustimye mazhoranty dlya modelnykh podprostranstv i argumenty vnutrennikh funktsii”, Funkts. anal. i ego pril., 40:4 (2006), 3–21 | MR | Zbl

[Bl1] Belov Yu. S., Khavin V. P., “K teoreme I. I. Privalova o preobrazovanii Gilberta lipshitsevykh funktsii”, Mat., fiz., anal., geom., 11:4 (2004), 380–407 | MR | Zbl

[Bl2] Belov Yu. S., “Kriterii dopustimosti mazhorant dlya modelnykh podprostranstv s bystro rastuschim argumentom porozhdayuschei vnutrennei funktsii”, Zap. nauch. semin. POMI, 345, 2007, 55–84 | MR

[Bl3] Belov Yu. S., “Modelnye funktsii s pochti predpisannym modulem”, Algebra i analiz, 20:2 (2008), 3–18 | MR

[D] Dyakonov K. M., “Moduli i argumenty analiticheskikh funktsii iz podprostranstv v $H^p$, invariantnykh dlya operatora obratnogo sdviga”, Sib. mat. zh., 31:6 (1990), 64–79 | MR

[HJ] Havin V., Jöricke B., The uncertainty principle in harmonic analysis, Ergeb. Math. Grenzgeb. (3), 28, Springer-Verlag, Berlin, 1994 | MR | Zbl

[HM1] Havin V. P., Mashreghi J., “Admissible majorants for model subspaces of $H^2$. I. Slow winding of the generating inner function”, Canad. J. Math., 55:6 (2003), 1231–1263 | MR | Zbl

[HM2] Havin V. P., Mashreghi J., “Admissible majorants for model subspaces of $H^2$. II. Fast winding of the generating inner function”, Canad. J. Math., 55:6 (2003), 1264–1301 | MR | Zbl

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

[N] Treatise on the shift operator, Grundlehren Math. Wiss., 273, Springer-Verlag, Berlin, 1986 | MR | MR