A spectral expansion for Schrödinger operator
Author
Bascanbaz-Tunca, Gülen
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/155010.4067/S0716-09172006000100005
Abstract
In this paper we consider the Schrödinger operator L generated inL²(R+) byy''+q(x)y= µy; x ∈ R+ := [0, ∞)subject to the boundary conditiony'(0)-hy(0)=0,where q is a complex valued function summable in [0, ∞ and h ≠ 0 is a complex constant, µ is a complex parameter. We have assumed thatholds which is the minimal condition that the eigenvalues and the spectral singularities of the operator L are finite with finite multiplicities. Under this condition we have given the spectral expansion formula for the operator L using an integral representation for the Weyl function of L. Moreover we also have investigated the convergence of the spectral expansion.