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Continuous spectra of
second-order differential operators
Don Barker Hinton |
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Vol. 33 (1970), No. 3, 641–643
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Abstract |
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We consider the differential operator l(y) = y′′ + qy, where q is a positive, continuously differentiable function defined on a ray [a,∞). The operator l determines, with appropriate restrictions, self-adjoint operators defined in the hilbert space ℒ2[a,∞) of quadratically summable, complexvalued functions on [a,∞). In this note, we prove that if L is such a selfadjoint operator, then the conditions q(t) →∞ and q′(t)q(t)−1∕2 → 0 as t →∞ are sufficient for the continuous spectrum C(L) of L to cover the entire real axis. |
Mathematical Subject Classification
Primary: 47.60
Secondary: 34.00
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Milestones
Received: 3 October 1969
Published: 1 June 1970
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Authors |
| Don Barker Hinton | |
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