On basicity of perturbed system of exponents in Lebesgue space with variable summability factor

In this paper, the system of exponents \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{ e^{i\lambda _n t} \} _{n \in Z} $\end{document} is considered, where {λn} ⊂ R has the following asymptotic form: λn = n − α sign n + O(|n|−β). Basis properties of this system in Lebesgue space with variable summability factor are investigated.