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Two separation criteria for second order ordinary or partial differential operators

Richard C. Brown;  Don B. Hinton — 1999

Mathematica Bohemica

We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in ℝ n . Also, for symmetric second-order ordinary differential operators we show that lim sup t → c ( p q ' ) ' / q 2 = θ < 2 where c is a singular point guarantees separation of - ( p y ' ) ' + q y on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that - Δ y + q y is separated on its minimal domain if q is superharmonic. For n = 1 the criterion...

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