On the basicity by riesz of the eigenvectors system of a correct restriction of the maximality linear operator

The work is devoted to the study of the similarity of a correct restriction to some self-adjoint operator in the case when the minimal operator is symmetric. The resulting theorem was applied to the SturmLiouville operator and the Laplace operator. It is shown that the spectrum of a non self-adjoint singularly perturbed operator is real and the corresponding system of eigenvectors forms a Riesz basis.

Keywords: Maximal (minimal) operator, correct restriction, correct extension, real spectrum, non self-adjoint operator.