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A Singular Boundary Value Problem for a Non-Self-Adjoint Differential Operator

Published online by Cambridge University Press:  20 November 2018

R. R. D. Kemp
R. R. D. Kemp*
Affiliation:
Queen's University Kingston
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If the differential expression l(y) = — y” + g(x)y generates a closed operator L on L2(— ∞, ∞), with domain D consisting of those functions y ∈ L2 with absolutely continuous derivatives and such that l(y) ∈ L2. The case where g(x) is real-valued has been extensively investigated and yields an expansion of any ƒ ∈ L2 in terms of the characteristic functions of L. We shall investigate the case where g is complex-valued.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 447 - 462
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Coddington, E. A. and Levinson, N., Theory of Ordinary Differential Equations (New York, 1955).Google Scholar
2. Naimark, M. A., Investigation of the spectrum and expansion in eigenfunctions of a non-self - adjoint differential operator of the second order on a semi-axis, Trudy Moskov Mat. Obsc, 3 (1954), 181 270.Google Scholar
3. Titchmarsh, E. C., Eigenf unction Expansions (Oxford, 1946).Google Scholar