On the eigenfunctions of Sturm--Liouville operators with potentials --- distributions

Artem Savchuk

paper

On the eigenfunctions of Sturm--Liouville operators with potentials --- distributions

arXiv:1003.3172

Abstract

In this paper we study a Sturm--Liouville operator $L y = - y " + q (x) y$ in the space $L_{2} [0, π]$ with Direchlet boundary conditions. Here the potential $q$ is a first order distribution: $q \in W_{2}^{- 1} [0, π]$ . Such operators were defined in our previous papers. Here we clerify two leading terms in asymptotic formulae for eigenfunctions of such operators and for functions of biorthogonal system.