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

Abstract

AbstractThis 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. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)