Copyright © 2009 Elgiz Bairamov and Nihal Yokus. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let L denote the operator generated in L2(R+) by Sturm-Liouville equation −y′′+q(x)y=λ2y, x∈R+=[0,∞), y′(0)/y(0)=α0+α1λ+α2λ2, where q is a complex-valued function and αi∈ℂ, i=0,1,2 with α2≠0. In this article, we investigate the eigenvalues and the spectral singularities of L and obtain analogs of Naimark and Pavlov conditions for L.