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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Model functions with nearly prescribed modulus

Author: Yu. S. Belov
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 20 (2008), nomer 2.
Journal: St. Petersburg Math. J. 20 (2009), 163-174
MSC (2000): Primary 30D50, 30D55
Published electronically: January 30, 2009
MathSciNet review: 2423994
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Abstract | References | Similar Articles | Additional Information

Abstract: 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 $ \vert f\vert\asymp \omega$. Certain conditions sufficient for strong admissibility are given 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, Petrodvorets, Universitetskiĭ Prospekt 20, St. Petersburg 198504, Russia

Keywords: Admissible function, Beurling--Malliavin theorem, model subspace, logarithmic integral
Received by editor(s): December 20, 2007
Published electronically: January 30, 2009
Additional Notes: Supported by RFBR, grant no. 06-01-00313
Article copyright: © Copyright 2009 American Mathematical Society