Article
Ufa Mathematical Journal
Volume 4, Number 1, pp. 58-64
On the distribution of indicators of unconditional exponential bases in spaces with a power weight
Isaev K.P., Trunov K.V.
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In the present paper we consider the existence of unconditional exponential bases in a space of locally integrable functions on a bounded interval of the real number line $ I $ satisfying $$ \| f \|: = \sqrt {\int _I | f (t) | ^ 2e ^ {-2h (t)} \, dt} <\infty, $$ where $ h (t) $ is a convex function on this interval. The lower estimate was obtained for the frequency of indicators of unconditional bases of exponentials when $I=(-1;1)$, $h(t)=-\alpha \ln (1-|t|)$, $\alpha > 0$.