Research Papers

On unconditional exponential bases in weighted spaces on interval of real axis

K. P. Isaev^ab, R. S. Yulmukhametov^ab, A. A. Yunusov<sup>b

a</sup> Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa, Russia
^b Bashkir State University, Ufa, Russia

Abstract: It is proved that if a weighted space $L_2(h)$ on the interval $(-1;1)$ admits an unconditional basis of exponentials, and the entire function that generates this basis satisfies a certain condition, then the space $L_2(h)$ is isomorphic (as a normed space) to the usual space $L_2$.

Keywords: Series of exponentials, unconditional basis, Hilbert space, entire functions.

Received: 10.01.2016

 English version: St. Petersburg Mathematical Journal, 2017, 28:5, 689–706

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