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Additional spectral properties of the fourth‐order Bessel‐type differential equation
Author(s) -
Everitt W. N.,
Kalf H.,
Littlejohn L. L.,
Markett C.
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410320
Subject(s) - mathematics , bessel function , real line , mathematical analysis , lebesgue integration , lebesgue measure , absolute continuity , measure (data warehouse) , hilbert space , differential operator , riemann–stieltjes integral , operator (biology) , pure mathematics , spectrum (functional analysis) , complex plane , eigenvalues and eigenvectors , integral equation , biochemistry , chemistry , physics , repressor , quantum mechanics , database , computer science , transcription factor , gene
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)