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

✍ Scribed by W. N. Everitt; H. Kalf; L. L. Littlejohn; C. Markett

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
177 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

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

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