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Ufimsk. Mat. Zh., 2016, Volume 8, Issue 4, Pages 90–99 (Mi ufa353)  

On unconditional exponential bases in weak weighted spaces on segment

K. P. Isaevab, A. V. Lutsenkob, R. S. Yulmukhametovab

a Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
b Bashkir State University, Ufa

Abstract: We show that the existence of unconditional exponential bases is not determined by the growth characteristics of weight function. In order to do this, we construct examples of convex weights with arbitrarily slow growth near the boundary such that unconditional exponential bases do not exist in the corresponding space.

Keywords: Hilbert spaces, entire functions, unconditional exponential bases, Riesz bases.

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English version:
Ufa Mathematical Journal, 2016, 8:4, 88–97 (PDF, 345 kB); https://doi.org/10.13108/2016-8-4-88

Bibliographic databases:

UDC: 517.5
MSC: 30B50, 30D20
Received: 30.05.2016

Citation: K. P. Isaev, A. V. Lutsenko, R. S. Yulmukhametov, “On unconditional exponential bases in weak weighted spaces on segment”, Ufimsk. Mat. Zh., 8:4 (2016), 90–99; Ufa Math. J., 8:4 (2016), 88–97

Citation in format AMSBIB
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\paper On unconditional exponential bases in weak weighted spaces on segment
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\vol 8
\issue 4
\pages 90--99
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\pages 88--97
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