Model functions with nearly prescribed modulus
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Yu. S. Belov
Translated by: S. V. Kislyakov - St. Petersburg Math. J. 20 (2009), 163-174
- DOI: https://doi.org/10.1090/S1061-0022-09-01042-5
- Published electronically: January 30, 2009
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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 $|f|\asymp \omega$. Certain conditions sufficient for strong admissibility are given in the case where $\Theta$ is meromorphic.References
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Bibliographic Information
- Yu. S. Belov
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Petrodvorets, Universitetskiĭ Prospekt 20, St. Petersburg 198504, Russia
- Email: j_b_juri_belov@mail.ru
- Received by editor(s): December 20, 2007
- Published electronically: January 30, 2009
- Additional Notes: Supported by RFBR, grant no. 06-01-00313
- © Copyright 2009 American Mathematical Society
- Journal: St. Petersburg Math. J. 20 (2009), 163-174
- MSC (2000): Primary 30D50, 30D55
- DOI: https://doi.org/10.1090/S1061-0022-09-01042-5
- MathSciNet review: 2423994