Geodesic
On unconditional exponential bases in weak weighted spaces on segment
Ufa mathematical journal, Tome 8 (2016) no. 4, pp. 88-97 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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K. P. Isaev; A. V. Lutsenko; R. S. Yulmukhametov. On unconditional exponential bases in weak weighted spaces on segment. Ufa mathematical journal, Tome 8 (2016) no. 4, pp. 88-97. http://geodesic.mathdoc.fr/item/UFA_2016_8_4_a5/

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