On basicity of exponential and trigonometric systems in grand Lebesgue spaces

Abstract

Basis properties of exponential and trigonometric systems in grand Lebesgue spaces Lp)(-7r, 7r) are studied. Based on a shift operator, we consider the subspace Gp)(-7r, 7r) of the space Lp)(-7r, 7r), where continuous functions are dense, and the boundedness of the singular operator in this subspace is proved. We establish the basicity of exponential system {eint}n is an element of Z for Gp)(-7r, 7r) and the basicity of trigonometric systems {sin nt}n is an element of N and {cos nt}n is an element of N0 for Gp)(0, 7r).