Abstract
In the classical space L 2(−π, π) there exists the unconditional basis {e kit} (k is integer). In the work we study the existence of unconditional bases in weighted Hilbert spaces L 2(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 L 2(h) if for some α < 0 (1 − |t|)α = O(e h(t)), t→±1.
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Isaev, K.P. On unconditional exponential bases in weighted spaces on interval of real axis. Lobachevskii J Math 38, 48–61 (2017). https://doi.org/10.1134/S1995080217010097
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DOI: https://doi.org/10.1134/S1995080217010097