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

Artem Savchuk

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arXiv · 1003.3172

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

Artem Savchuk

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Abstract

In this paper we study a Sturm--Liouville operator $Ly=-y"+q(x)y$ 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.

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Artem Savchuk. 2010-03-16. On the eigenfunctions of Sturm--Liouville operators with potentials --- distributions. https://arxiv.org/abs/1003.3172

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