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This article is cited in 6 scientific papers (total in 6 papers)
On absence conditions of unconditional bases of exponents
R. A. Bashmakov, A. A. Makhota, K. V. Trounov Bashkir State University, Zaki Validi str., 32, 450076, Ufa, Russia
Abstract:
In the classical space $L^2(-\pi,\pi)$ there exists the unconditional basis $\{e^{ikt}\}$ ($k$ is integer). In the work we study the existence of unconditional bases in weighted Hilbert spaces $L^2(I,\exp h)$ of the functions square integrable on an interval $I$ in the real axis with the weight $\exp(- h)$, where $h$ is a convex function. We obtain conditions showing that unconditional bases of exponents can exist only in very rare cases.
Keywords:
Riesz bases, unconditional bases, series of exponents, Hilbert space, Fourier–Laplace transform.
Received: 01.04.2015
Citation:
R. A. Bashmakov, A. A. Makhota, K. V. Trounov, “On absence conditions of unconditional bases of exponents”, Ufimsk. Mat. Zh., 7:2 (2015), 19–34; Ufa Math. J., 7:2 (2015), 17–32
Linking options:
https://www.mathnet.ru/eng/ufa276https://doi.org/10.13108/2015-7-2-17 https://www.mathnet.ru/eng/ufa/v7/i2/p19
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Abstract page: | 383 | Russian version PDF: | 148 | English version PDF: | 11 | References: | 47 |
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