Abstract

Perturbation Theory for Ordinary Differential Equations D. Hinton The theory of relative boundedness or compactness plays a useful role in the spectral theory of linear operators. For example, the Kato-Rellich theorem states that if A is self-adjoint and B is a symmetric A-bounded operator with relative bound less than one, then A+B is self-adjoint; further A+B is bounded below if A is. Relative compactness preserves the essential spectrum and Fredholm index. In this talk operators and their perturbations will be considered which are determined by singular ordinary differential expressions. For several classes of operators necessary and sufficient conditions will be given for a perturbation to be relatively bounded or compact. Both maximal and minimal operators are examined. In the case of a limit-circle endpoint, it is found that the criteria have a somewhat different structure than for the limit-point endpoint.

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