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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Admissibility of majorants in certain model subspaces: Necessary conditions


Author: Yu. S. Belov
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 20 (2008), nomer 4.
Journal: St. Petersburg Math. J. 20 (2009), 507-525
MSC (2000): Primary 30D50, 30D55, 30D20
Published electronically: June 1, 2009
MathSciNet review: 2473742
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Abstract: 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 $ \vert f\vert\le \omega$. Some conditions necessary for admissibility are presented in the case where $ \Theta$ is meromorphic.


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Additional Information

Yu. S. Belov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 20, Petrodvorets, 198504 St. Petersburg, Russia
Email: j_b_juri_belov@mail.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-09-01059-0
PII: S 1061-0022(09)01059-0
Keywords: Blaschke product, model subspace, admissible majorant, Beurling--Malliavin theorem
Received by editor(s): February 20, 2008
Published electronically: June 1, 2009
Additional Notes: Supported by RFBR (grant no. 06–01–00313).
Article copyright: © Copyright 2009 American Mathematical Society