On the basicity of eigenfunctions of a second-order differential operator with a discontinuity point in weighted Lebesgue spaces
Journal: Proceedings of the Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan
Year: 2020

We propose a new method for proving that eigenfunctions of non-self-adjoint differential operators in weighted Lebesgue spaces form a basis. A spectral problem for a second-order discontinuous differential operator on a finite interval of the real axis with one discontinuity point, which divides the interval into commensurable parts, is considered. The spectral parameter linearly enters both the equation and the transmission condition. Such problems arise when studying the problem of oscillation