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XIV.—On Bounded Integral Operators in the Space of Integrable-Square Functions*

Published online by Cambridge University Press:  14 February 2012

R. S. Chisholm  and
W. N. Everitt
R. S. Chisholm
Affiliation:
Department of Mathematics, University of Dundee
W. N. Everitt
Affiliation:
Department of Mathematics, University of Dundee
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Extract

§ 1. Let L2(0, ∞) denote the Hilbert space of Lebesgue measurable, integrable-square functions on the half-line [0, ∞).

Integral operators of the form

acting on the space L2 (0, ∞) occur in the theory of ordinary differential equations; see for example the book by E. C. Titchmarsh [4; § 2.6]. It is important to establish when operators of this kind are bounded; see the book by A. E. Taylor [3; § 4.1 and §§4.11, 4.12 and § 4.13].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 69 , Issue 3 , 1971 , pp. 199 - 204
Copyright
Copyright © Royal Society of Edinburgh 1971

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References

References to Literature

[1]Chaudhuri, J. and Everttt, W. N., 1969. ‘On the spectrum of ordinary second order differential operators’, Proc. Roy. Soc. Edinb., 68A, 95–119.Google Scholar
[2]Everitt, W. N., 1963. ‘A note on the self-adjoint domains of second order differential equations’, Q. Jl Math., 14, 41–45.CrossRefGoogle Scholar
[3]Taylor, A. E., 1958. Introduction to Functional Analysis. New York: Wiley.Google Scholar
[4]Titchmarsh, E. C., 1962. Eigenfunction Expansions, Part I. O.U.P.Google Scholar