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St. Petersburg Mathematical Journal

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

 
 

 

On unconditional bases of exponentials in weighted spaces on an interval of the real axis


Authors: K. P. Isaev, R. S. Yulmukhametov and A. A. Yunusov
Translated by: N. N. Osipov
Original publication: Algebra i Analiz, tom 28 (2016), nomer 5.
Journal: St. Petersburg Math. J. 28 (2017), 689-706
MSC (2010): Primary 30B50
DOI: https://doi.org/10.1090/spmj/1467
Published electronically: July 25, 2017
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Abstract: It is proved that if a weighted space $ L_2(h)$ on the interval $ (-1;1)$ admits an unconditional basis of exponentials, and the entire function that generates this basis satisfies a certain condition, then the space $ L_2(h)$ is isomorphic (as a normed space) to the usual space $ L_2$.


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Additional Information

K. P. Isaev
Affiliation: Institute of mathematics with computer center, Ufa scientific center RAS, 112 Chernyshevskiĭ str., 450008 Ufa; Bashkir State University, 32 Zaki Validi str., 450076 Ufa, Russia
Email: orbit81@list.ru

R. S. Yulmukhametov
Affiliation: Institute of mathematics with computer center, Ufa scientific center RAS, 112 Chernyshevskiĭ str., 450008 Ufa; Bashkir State University, 32 Zaki Validi str., 450076 Ufa, Russia
Email: yulmukhametov@mail.ru

A. A. Yunusov
Affiliation: Bashkir State University, 32 Zaki Validi str., 450076 Ufa, Russia
Email: mc.yunusov@gmail.com

DOI: https://doi.org/10.1090/spmj/1467
Keywords: Series of exponentials, unconditional basis, Hilbert space, entire functions
Received by editor(s): January 10, 2016
Published electronically: July 25, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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