Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-19T10:31:30.800Z Has data issue: false hasContentIssue false
  • English
  • Français

On a quadratic integral inequality*

Published online by Cambridge University Press:  14 November 2011

R. J. Amos  and
W. N. Everitt
R. J. Amos
Affiliation:
Department of Mathematics, University of Dundee
W. N. Everitt
Affiliation:
Department of Mathematics, University of Dundee
Get access Rights & Permissions [Opens in a new window]

Synopsis

The inequality considered is

where p and q are given real-valued coefficients on the interval [a, b), with b ≦ ∝, of the real line; here D is a linear manifold of the Hilbert function space L2(a, b), and μ is a real number characterised in terms of the spectrum of a uniquely determined self-adjoint differential operator in L2(a, b).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 3-4 , 1978 , pp. 241 - 256
Copyright
Copyright © Royal Society of Edinburgh 1978

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.)

Footnotes

*

This paper was assisted in publication by a grant from the Carnegie Trust for the Universities of Scotland.

References

1 Akhiezer, N. I. and Glazman, I. M.. Theory of linear operators in Hilbert space, 1 (New York: Ungar, 1961).Google Scholar
2 Bradley, 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
3 Bradley, J. S. and Everitt, W. N.. A singular integral inequality on a bounded interval. Proc. Amer. Math. Soc. 61 (1976), 29–35.CrossRefGoogle Scholar
4 Evans, W. D.. On limit-point and Dirichlet-type results for second-order differential expressions. Lecture Notes in Mathematics 564 (Berlin: Springer, 1976).Google Scholar
5 Everitt, W. N.. On the strong limit-point condition of second-order differential expressions. Proc. Internal. Conf. Differential Equations, Los Angeles, 287–307 (New York: Academic Press, 1975).Google Scholar
6 Everitt, W. N.. A note on the Dirichlet condition for second-order differential expressions. Canad. J. Math. 28 (1976), 312–320.CrossRefGoogle Scholar
7 Everitt, W. N.. Spectral theory of the Wirtinger inequality. Lecture Notes in Mathematics 564 (Berlin: Springer, 1976).Google Scholar
8 Kalf, H.. Remarks on some Dirichlet type results for semibounded Sturm-Liouville operators. Math. Ann. 210 (1974), 197–205.CrossRefGoogle Scholar
9 Kato, T.. Perturbation theory for linear operators (Berlin: Springer, 1966).Google Scholar
10 Kwong, M. K.. Note on the strong limit point condition of second order differential expressions. Quart. J. Math. Oxford Ser., in press.Google Scholar
11 Naimark, M. A.. Linear differential operators, II (New York: Ungar, 1968).Google Scholar
12 Sears, D. S. and Wray, S. D.. An inequality of C. R. Putnam involving a Dirichlet functional. Proc. Roy. Soc. Edinburgh Sect. A 75 (1976), 199–207.CrossRefGoogle Scholar