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

Artem Savchuk

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

Spectral Theory 2010-03-17 v1

Authors: Artem Savchuk

Abstract

In this paper we study a Sturm--Liouville operator $Ly=-y"+q(x)y$ in the space $L_2[0,\pi]$ with Direchlet boundary conditions. Here the potential $q$ is a first order distribution: $q\in W_2^{-1}[0,\pi]$ . 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.

Keywords

Sturm-Liouville operator distribution potential eigenfunction asymptotic formula Dirichlet boundary condition biorthogonal system

Cite

@article{arxiv.1003.3172,
  title  = {On the eigenfunctions of Sturm--Liouville operators with potentials --- distributions},
  author = {Artem Savchuk},
  journal= {arXiv preprint arXiv:1003.3172},
  year   = {2010}
}

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