On basicity of exponential and trigonometric systems in grand Lebesgue spaces

Authors : Migdad ISMAİLOV, Yusuf ZEREN, Kader ŞİMŞİR ACAR, Ilahe F ALİYAROVA

Pages : 1577-1587

Doi:10.15672/hujms.1076849

View : 24 | Download : 9

Publication Date : 2022-12-01

Article Type : Research Paper

Abstract :Basis properties of exponential and trigonometric systems in grand Lebesgue spaces $ L_{p);} insert ignore into journalissuearticles values(-\pi,\pi); $ are studied. Based on a shift operator, we consider the subspace $G_{p);} insert ignore into journalissuearticles values(-\pi,\pi);$ of the space $ L_{p);} insert ignore into journalissuearticles values(-\pi,\pi); $, where continuous functions are dense, and the boundedness of the singular operator in this subspace is proved. We establish the basicity of exponential system $ \{{e^{int}}\}_{n\in Z}$ for $G_{p);} insert ignore into journalissuearticles values(-\pi,\pi);$ and the basicity of trigonometric systems $ \{{\sin{nt}}\}_{n\in N }$ and $ \{{\cos{nt}}\}_{n\in N_0}$ for $G_{p);} insert ignore into journalissuearticles values(0,\pi);$.
Keywords : grand Lebesgue space, exponential system, minimality, density, basis