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2.—Semi-bounded Second-order Differential Operators

Published online by Cambridge University Press:  14 February 2012

M. S. P. Eastham
M. S. P. Eastham
Affiliation:
Department of Mathematics, Chelsea College, University of London.
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Synopsis

Differential operators generated by the differential expression My(x) = —y″(x)+q(x)y(x) in L2(0, ∞) are considered. It is assumed that

is bounded for all x in [0, ∞) and some fixed ω > 0. The operators are shown to be bounded below and an estimate for the lower bound is obtained in terms of q(x). In the case where q(x) is LP (0, ∞) for some p ≧ 1, the results are compared with recent ones of W. N. Everitt. Some comments are made on the best-possible nature of the results.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 72 , Issue 1 , 1974 , pp. 9 - 16
Copyright
Copyright © Royal Society of Edinburgh 1974

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References

References to Literature

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