Two separation criteria for second order ordinary or partial differential operators

Brown, R. C. ; Hinton, D. B.

Mathematica Bohemica, Tome 124 (1999) no. 2-3, pp. 273-292.

Résumé

We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in $\Bbb R^n$. Also, for symmetric second-order ordinary differential operators we show that $\limsup_{t\to c} (pq')'/q^2=\theta2$ where $c$ is a singular point guarantees separation of $-(py')'+qy$ on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that $-\Delta y+qy$ is separated on its minimal domain if $q$ is superharmonic. For $n=1$ the criterion is used to give examples of a separation inequality holding on the domain of the minimal operator in the limit-circle case.

Détail

DOI : 10.21136/MB.1999.126251

Classification : 26D10, 34B05, 34C05, 34L05, 34L40, 35B45, 35P05, 47E05, 47F05
Keywords: separation; ordinary or partial differential operator; limit-point; essentially selfadjoint