On unconditional exponential bases in weak weighted spaces on segment

Authors

  • K.P. Isaev
    Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
    Bashkir State University, Ufa
  • A.V. Lutsenko
    Bashkir State University, Ufa
  • R.S. Yulmukhametov
    Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
    Bashkir State University, Ufa

DOI:

https://doi.org/10.13108/2016-8-4-88

Keywords:

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

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.

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Published

20.12.2016

Issue

Vol. 8 No. 4 (2016): Ufa Mathematical Journal 2016, volume 8 , issue 4

Section

Article