Vol. 33, No. 3, 1970

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Continuous spectra of second-order differential operators

Don Barker Hinton

Vol. 33 (1970), No. 3, 641–643
Abstract

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 2[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)12 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
Milestones
Received: 3 October 1969
Published: 1 June 1970
Authors
Don Barker Hinton