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Limit circle criteria for 2nth order differential operators

Published online by Cambridge University Press:  20 January 2009

Ronald I. Becker
Ronald I. Becker
Affiliation:
Department of MathematicsUniversity of Cape TownRondebosch 7700Republic of South Africa
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A formally self-adjoint differential operator L is said to be of limit circle type at infinity if its highest order coefficient is zero-free and all solutions x of L(x) = 0 are square-integrable on [a, ∞). (We will drop reference to “at infinity” in what follows.)

For the second-order case

Dunford and Schwartz (3) p. 1409 prove that given

then L is of limit circle type if and only if

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 1 , February 1981 , pp. 59 - 72
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

REFERENCES

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