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

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

2010-03-16

arxiv.org/abs/1003.3172v1

Mathematics

Spectral Theory

Scientific paper

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.

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