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Subsequences of zeros for Bernstein spaces and the completeness of systems of exponentials in spaces of functions on an interval


Authors: B. N. Khabibullin, G. R. Talipova and F. B. Khabibullin
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 26 (2014), nomer 2.
Journal: St. Petersburg Math. J. 26 (2015), 319-340
MSC (2010): Primary 30B50; Secondary 42C30
DOI: https://doi.org/10.1090/S1061-0022-2015-01340-X
Published electronically: February 3, 2015
MathSciNet review: 3242038
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \sigma >0$. The symbol $ B_\sigma ^\infty $ denotes the space of all entire functions of exponential type not exceeding $ \sigma $ that are bounded on the real axis. Various exact descriptions of uniqueness sequences for the Bernstein spaces $ B_\sigma ^\infty $ are given in terms of $ \sigma $ and the Poisson and Hilbert transformations. These descriptions lead to completeness criteria for systems of exponentials (up to one or two members) in various classical function spaces on an interval (closed or open) of length $ d$.


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Additional Information

B. N. Khabibullin
Affiliation: Bashkir State University, ul. Zaki Validi 32, Ufa 450074, Bashkortostan, Russia
Email: Khabib-Bulat@mail.ru

G. R. Talipova
Affiliation: Bashkir State University, ul. Zaki Validi 32, Ufa 450074, Bashkortostan, Russia

F. B. Khabibullin
Affiliation: Bashkir State University, ul. Zaki Validi 32, Ufa 450074, Bashkortostan, Russia

DOI: https://doi.org/10.1090/S1061-0022-2015-01340-X
Keywords: Entire function, Bernstein space, sequence of uniqueness, completeness of exponentials, Poisson integral, Hilbert transformation
Received by editor(s): February 4, 2012
Published electronically: February 3, 2015
Additional Notes: Supported by RFBR (grant no. 13-01-00030a) and by the Federal targeted program “Scientific and pedagogical staff of innovative Russia” (contract no. 14.B37.21.0358)
Article copyright: © Copyright 2015 American Mathematical Society