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

Abstract

In the classical space L2(−π, π) there exists the unconditional basis {ekit} (k is integer). In the work we study the existence of unconditional bases in weighted Hilbert spaces L2(h) of the functions square integrable on an interval (−1, 1) with the weight exp(−h), where h is a convex function. We prove that there exist no unconditional exponential bases in space L2(h) if for some α < 0 (1 − |t|)α = O(eh(t)), t→±1.