Non-Self-Adjointness of Operators with Small Diffusion.

The article focuses on non-self-adjointness of operators with small diffusion. The question of whether the constructed (formal) asymptotic eigenfunctions and eigenvalues approximate some exact eigenfunctions and eigenvalues of the operator L turns out to be very nontrivial, and the answer to this question is still unknown. A similar question has been discussed for numerous problems of quantum and wave mechanics.