13.—On Some Results of Everitt and Giertz
- 1 January 1973
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences
- Vol. 71 (2) , 151-158
- https://doi.org/10.1017/s0080454100009316
Abstract
The differential expression Mf = −f″+qf, on a half-line [a, ∞), is said to be ‘separated’ in L2(a, ∞) if the collection of all functions f ∈ L2(a, ∞) such that Mf is defined and also in L2(a, ∞), has the property that both the terms f″ and qf are separately in L2(a, ∞). When q is positive and differentiable on [a, ∞) this paper obtains sufficient conditions on the coefficient q for M to be separated; these take the form of bounds for q′q−3/2 on [a, ∞).Keywords
This publication has 6 references indexed in Scilit:
- On Some Properties of the Domains of Powers of Certain Differential OperatorsProceedings of the London Mathematical Society, 1972
- On Some Properties of the Powers of a Formally Self-Adjoint Differential ExpressionProceedings of the London Mathematical Society, 1972
- Some inequalities associated with certain ordinary differential operatorsMathematische Zeitschrift, 1972
- Some Properties of the Domains of Certain Differential OperatorsProceedings of the London Mathematical Society, 1971
- On the Solutions in L 2 (−∞, ∞) of y ″ + (λ − q (x ))y = 0 when q is Rapidly IncreasingProceedings of the London Mathematical Society, 1964
- Asymptotic formulae for linear oscillationsProceedings of the Glasgow Mathematical Association, 1956