Hostname: page-component-7479d7b7d-pfhbr Total loading time: 0 Render date: 2024-07-13T17:57:58.376Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Nature of the Spectrum of Singular Second Order Linear Differential Equations

Published online by Cambridge University Press:  20 November 2018

E. A. Coddington  and
N. Levinson
E. A. Coddington
Affiliation:
Massachusetts Institute of Technology
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let p(x) > 0, q(x) be two real-valued continuous functions on . Suppose that the differential equation with the real parameter λ

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 335 - 338
Copyright
Copyright © Canadian Mathematical Society 1951

References

[1] Hartman, P. and Wintrier, A., An oscillation theorem for continuous spectra, Proc. Nat. Acad. Sci., vol. 33 (1947), 376–379.Google Scholar
[2] Hartman, P., A separation theorem for continuous spectra, Amer. J. Math., vol. 71 (1949), 650–662.Google Scholar
[3] Levinson, N., A simplified proof of the expansion theorem for singular second order linear differential equations, Duke Math. J. vol. 18 (1951), 57–71.Google Scholar
[4] Titchmarsh, E. C., Eigenfunction expansions associated with second-order differential equations, (Oxford, 1946).Google Scholar
[5] Weyl, H., Ueber beschränkte quadratische Formen, deren Differenz vollstetig ist, Rend. Circ. Palermo, vol. 27 (1909), 373–392.Google Scholar
[6] Weyl, H., Ueber gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkurlicher Funktionen, Math. Ann., vol. 68 (1910), 222–269.Google Scholar