Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-28T18:22:33.450Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Boundary value problems

Published online by Cambridge University Press:  26 February 2010

D. J. Gilbert  and
B. J. Harris
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.
Get access

Extract

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

with the boundary condition

MSC classification

Secondary: 34B24: Sturm-Liouville theory
Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 327 - 337
Copyright
Copyright © University College London 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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), 2648–2658.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), 333–348.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), 181–197.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), 573–582.CrossRefGoogle Scholar
5.Eastham, M. S. P.. On the location of spectral concentration for Sturm-Liouville problems with rapidly decaying potential. Mathematika, 45 (1998), 25–36.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), 25–34.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), 355–364.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), 149–161.CrossRefGoogle Scholar
10.Titchmarsh, E. C.. Eigenfunction Expansions, Part 1 (2nd Edition). (Clarendon Press, Oxford, 1962).Google Scholar