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    On basicity of exponential and trigonometric systems in grand Lebesgue spaces
    (Hacettepe University, 2022) Ismailov, Migdad I.; Zeren, Yusuf; Acar, Kader Simsir; Aliyarova, Ilahe F.
    Basis properties of exponential and trigonometric systems in grand Lebesgue spaces Lp) (??, ?) are studied. Based on a shift operator, we consider the subspace Gp) (??, ?) of the space Lp) (??, ?), 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?Z for Gp) (??, ?) and the basicity of trigonometric systems {sin nt}n?N and {cos nt}n?N0 for Gp) (0, ?).