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Bounds for the points of spectral concentration of Sturm–Liouville problems

Published online by Cambridge University Press:  26 February 2010

D. J. Gilbert
Affiliation:
School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland.
B. J. Harris
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115-2888, U.S.A.
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Extract

§1. Introduction. We consider the spectral function ρα(λ) associated with the Sturm–Liouville equation

with the boundary condition

MSC classification

Type
Research Article
Copyright
Copyright © University College London 2000

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References

1.Brandas, E., Rittby, M. and Elander, N.. Titchmarsh-Weyl theory and its relations to scattering theory: spectral densities and cross sections; theory and applications. J. Math. Phys., 26 (1985), 26482658.CrossRefGoogle Scholar
2.Brown, B. M., Eastham, M. S. P. and McCormick, D. K. R.. Spectral concentration and rapidly decaying potentials. J. Comp. Appl. Math., 81 (1997), 333348.CrossRefGoogle Scholar
3.Brown, B. M., Eastham, M. S. P. and McCormick, D. K. R.. Absolute continuity and spectral concentration for slowly decaying potentials. J. Comp. Appl. Math., 94 (1998), 181197.CrossRefGoogle Scholar
4.Eastham, M. S. P.. The asymptotic nature of spectral functions in Sturn-Liouville problems with continuous spectra. J. Math. Analysis Appl., 213 (1997), 573582.CrossRefGoogle Scholar
5.Eastham, M. S. P.. On the location of spectral concentration for Sturm-Liouville problems with rapidly decaying potential. Mathematika, 45 (1998), 2536.CrossRefGoogle Scholar
6.Gilbert, D. J. and Harris, B. J.. Connection formulae for spectral functions associated with singular Sturm-Liouville equations. Proc. Royal Soc. Edinburgh, 130A (2000), 2534.CrossRefGoogle Scholar
7.Gilbert, D. J. and Harris, B. J.. On the recovery of differential equation from its spectral functions. J. Math. Analysis Appl. 262 (2001), 355364.CrossRefGoogle Scholar
8.Hardy, G. H.. A Course of Pure Mathematics. Cambridge University Press (Cambridge, 1958).Google Scholar
9.Harris, B. J.. The form of the spectral functions associated with Sturm-Liouville problems with continuous spectrum. Mathematika, 44 (1997), 149161.CrossRefGoogle Scholar
10.Titchmarsh, E. C.. Eigenfunction Expansions, Part 1 (2nd Edition). (Clarendon Press, Oxford, 1962).Google Scholar