Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-27T19:33:58.172Z Has data issue: false hasContentIssue false
  • English
  • Français

18.—An Inequality of C. R. Putnam involving a Dirichlet Functional

Published online by Cambridge University Press:  14 February 2012

D. B. Sears  and
S. D. Wray
D. B. Sears
Affiliation:
Department of Mathematics, University of the Witwatersrand.
S. D. Wray
Affiliation:
Department of Mathematics, University of the Witwatersrand.
Get access Rights & Permissions [Opens in a new window]

Synopsis

An inequality of C. R. Putnam involving a Dirichlet functional in the singular theory of the Sturm-Liouville differential equation is generalised. The corresponding result for the Sturm-Liouville theory over a compact interval is established and this is extended to the singular case by means of a Tauberian argument.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 75 , Issue 3 , 1976 , pp. 199 - 207
Copyright
Copyright © Royal Society of Edinburgh 1976

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

REFERENCES

1Bradley, J. S. and Everitt, W. N.. Inequalities associated with regular and singular problems in the calculus of variations. Trans. Amer. Math. Soc. 182 (1973), 303–321.CrossRefGoogle Scholar
2Hille, E.. Lectures on ordinary differential equations (Reading, Massachusetts: Addison-Wesley, 1969).Google Scholar
3Kalf, H.. Remarks on some Dirichlet type results for semibounded Sturm-Liouville operators. Math. Ann. 210 (1974), 197–205.CrossRefGoogle Scholar
4Putnam, C. R.. An application of spectral theory to a singular calculus of variations problem. Amer. J. Math. 70 (1948), 780–803.CrossRefGoogle Scholar
5Sears, D. B.. Integral transforms and eigenfunction theory, I. Quart. J. Math. Oxford Ser. 5 (1954), 47–58.CrossRefGoogle Scholar
6Titchmarsh, E. C.. The theory of functions, 2nd edn (London: O.U.P., 1952).Google Scholar
7Titchmarsh, E. C.. Eigenfunction expansions associated with second-order differential equations, I, 2nd edn (Oxford: O.U.P., 1962).CrossRefGoogle Scholar