Article

    Ufa Mathematical Journal
    Volume 7, Number 2, pp. 17-32

    On absence conditions of unconditional bases of exponents


    Bashmakov R.A., Makhota A.A., Trunov K.V.

    DOI:10.13108/2015-7-2-17

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    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.