Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-12-02T19:50:46.697Z Has data issue: false hasContentIssue false
  • English
  • Français

Molchanov's Discrete Spectra Criterion for a Weighted Operator

Published online by Cambridge University Press:  20 November 2018

Don B. Hinton
Don B. Hinton*
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37916
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.

We consider the second-order operator

1

where the coefficients are real continuous functions on an interval ℐ with w and p positive. The operator is assumed singular at only one endpoint which we take to be either 0 (finite singularity) or ∞ (infinite singularity). Let be the Hilbert space of all complex-valued, measurable functions f satisfying

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 4 , 01 December 1979 , pp. 425 - 431
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Dunford, N. and Schwarz, J. T., Linear operators, II. New York: Interscience, 1963.Google Scholar
2. Glazman, I. M., Direct methods of qualitative spectral analysis of singular differential operators. Jerusalem: I.P.S.T., 1965.Google Scholar
3. Hinton, D. and Lewis, R., Singular differential operators with spectra discrete and bounded below, submitted to Proc. Royal Soc. Edinburgh.Google Scholar
4. Naimark, M. A., Linear differential operators: Part II. New York: Ungar, 1968.Google Scholar