On Stability of Bases From Perturbed Exponential Systems in Orlicz Spaces

摘要

In this article, perturbed exponential system e iλnt n∈Z , (where {λn} is some sequence of real numbers), is considered in the Orlicz space LM (−π, π). We find a condition on the sequence {λn}, which is sufficient for the above system to form a basis for LM (−π, π). We establish an analogue of classical Levinson theorem on the replacement of a finite number of elements of this system by other elements. Our results are the analogues of the corresponding results obtained for Lebesgue spaces Lp, 1 ≤ p ≤ +∞. We also establish an analogue of classical Levinson theorem on the completeness of above system in the spaces Lp, 1 ≤ p ≤ +∞.