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Limit circle criteria for 2nth order differential operators
Published online by Cambridge University Press: 20 January 2009
Extract
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
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- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 1 , February 1981 , pp. 59 - 72
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- Copyright © Edinburgh Mathematical Society 1981
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