On unconditional exponential bases in weighted spaces on real axis

A. A. Yunusov

Bashkir State University, Ufa, Russia

Abstract: We prove that if there exists an unconditional exponential basis in integral weighted functional space on interval $(-1,1)$ and the entire generating function satisfies some condition, then space $L_2(h)$ as a normed space is isomorphic to classical space $L_2$.

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

UDC: 517.5

MSC: 30D20

Received: 02.08.2015

 English version: Ufa Mathematical Journal, 2015, 7:3, 108–118

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