On unconditional exponential bases in weighted spaces on interval of real axis
- Authors: Isaev K.P.1,2
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Affiliations:
- Institute of Mathematics with Computer Center
- Bashkir State University
- Issue: Vol 38, No 1 (2017)
- Pages: 48-61
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198630
- DOI: https://doi.org/10.1134/S1995080217010097
- ID: 198630
Cite item
Abstract
In the classical space L2(−π, π) there exists the unconditional basis {ekit} (k is integer). In the work we study the existence of unconditional bases in weighted Hilbert spaces L2(h) of the functions square integrable on an interval (−1, 1) with the weight exp(−h), where h is a convex function. We prove that there exist no unconditional exponential bases in space L2(h) if for some α < 0 (1 − |t|)α = O(eh(t)), t→±1.
About the authors
K. P. Isaev
Institute of Mathematics with Computer Center; Bashkir State University
Author for correspondence.
Email: orbit81@list.ru
Russian Federation, ul. Chernyshevskogo 112, Ufa, 450008; ul. Zaki Validi 32, Ufa, 450076