On basicity of exponential and trigonometric systems in grand Lebesgue spaces

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