Nonstandard Lagrangian Singularities and Asymptotic Eigenfunctions of the Degenerating Operator \( - {d \over {dx}}D\left( x \right){d \over {dx}}\)

Abstract

We express the asymptotic eigenfunctions of the operator \( - {d \over {dx}}D\left( x \right){d \over {dx}}\) that degenerates at the endpoints of an interval in terms of the modified Maslov canonical operator introduced in our previous studies.