On the Davies Formula for the Distribution of Eigenvalues of a Non-Self-Adjoint Differential Operator

In this paper, we analyze conditions under which the spectrum of Sturm–Liouville operator on a certain smooth curve is localized near countable number rays. case where potential piecewise analytical, an asymptotic eigenvalues found for each series corresponding ray. The result obtained allows one to generalize well-known formula distribution function stated by Davies in finite localization