Document Type

Article

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This item is available under a Creative Commons License for non-commercial use only

Disciplines

1.1 MATHMATICS

Publication Details

Journal of differential equations, Vol 201, 2004. pp 139-159

Abstract

We consider the linear, second-order, differential equation (∗) with the boundary condition (∗∗)

We suppose that q(x) is real-valued, continuously differentiable and that q(x)→0 as x→∞ with q∉L1[0,∞). Our main object of study is the spectral function ρα(λ) associated with () and (). We derive a series expansion for this function, valid for λ⩾Λ0 where Λ0 is computable and establish a Λ1, also computable, such that () and () with α=0, have no points of spectral concentration for λ⩾Λ1. We illustrate our results with examples. In particular we consider the case of the Wigner–von Neumann potential.

DOI

https://doi.org/10.1016/j.jde.2003.10.028


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