Additional spectral properties of the fourth-order Bessel-type differential equation

This paper discusses the spectral properties of the self-adjoint differential operator generated by the fourth-order Bessel-type differential expression, as defined by Everitt and Markett in 1994, in a Lebesgue-Stieltjes Hilbert function space. This space involves functions defined on the real line; the Lebesgue-Stieltjes measure is locally absolutely continuous on the real line, with the origin removed; the origin itself has strictly positive measure. It is shown that there is a unique such self-adjoint operator; this operator has no eigenvalues but has a continuous spectrum on the positive half-line of the spectral plane. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.