On the basicity of one trigonometric system in Orlicz spaces

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Bilalov B., SEZER Y., Ildiz U., Hagverdi T.

Transactions Issue Mathematics, Azerbaijan National Academy of Sciences, vol.44, no.1, pp.31-40, 2024 (Scopus) identifier


In this article it is considered the trigonometric system, which is the collection of eigenfunction of the ordinary differential operator second order with nonlocal boundary condition. It is considered the Orlicz space on the segment (0, 2π). It is established that if the Boyd indexes of this space belong to the interval (0, 1) then the considered system forms a basis in this space. This system was used by several mathematics in the study of solvability and construction of solution of one second order degenerate elliptic equation with nonlocal boundary condition.