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Bessel sequences with finite upper density in de Branges spaces

Author: Yu. Belov
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 27 (2015), nomer 4.
Journal: St. Petersburg Math. J. 27 (2016), 599-607
MSC (2010): Primary 46E22
Published electronically: June 2, 2016
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Abstract: The de Branges spaces are described in which every real Bessel sequence $ \Lambda $ has finite upper density. The description is in terms of the spectral measure of the space in question.

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Additional Information

Yu. Belov
Affiliation: St. Petersburg State University, Chebysev Laboratory, Ul′yanovskaya 3, 198504 St. Petersburg, Russia

Keywords: Bessel sequences, de Branges spaces, Hilbert transform
Received by editor(s): April 16, 2015
Published electronically: June 2, 2016
Additional Notes: The author was supported by the Russian Scientific Foundation, grant no. 14-41-00010
Article copyright: © Copyright 2016 American Mathematical Society