On basicity of the system of eigenfunctions of one discontinuous spectral problemfor second order differential equation for grand-Lebesgue space

Abstract

Basicity of the system of eigenfunctions of some\textbf{ }discontinuous spectral problem for a second order differential equation with spectral parameter in boundary condition for grand-Lebesgue space $L_{p)} (-1;1)$ is studied in this work. Since the space is nonseparable, a subspace suitable for the spectral problem is defined. The subspace $G_{p)} (-1;1)$ of $L_{p)} (-1;1)$ generated by shift operator is considered. Basicity of the system of eigenfunctions for the space $G_{p)} (-1;1)\oplus C$, $1

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