Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential

For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm–Liouville operator A = sign(x)(−Δ+V(x)) accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.

On a class of nonselfadjoint periodic boundary value problems with discrete real spectrum

In a previous paper (J. of Differential Equations, Vol. 249 (2010), 3081-3098) we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the associated resolvent operator.

Determinants of pollution: what do we really know?

The recent literature proposes many variables as significant determinants of pollution. This paper gives an overview of this literature and asks which of these factors have an empirically robust impact on water and air pollution. We apply Extreme Bound Analysis (EBA) on a panel of up to 120 countries covering the period 1960–2001. We find supportive evidence of the existence of the environmental Kuznets curve for water pollution. Furthermore, mainly variables capturing the economic structure of a country affect air and water pollution.