On positive differential operators (deficiency indices, factorization, perturbations)
Fedor Semenovich Rofe-Beketov · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1984
Synopsis A short survey is given of some recent results. The perturbations and stability of discrete spectrum and the problems of resolvent convergence of densely or non-densely defined elliptic differential operators are considered. The Courant theorem on variations of the domain is generalized. In connection with Berezanskiy's theorem on essential self-adjointness, the test for the finite velocity of propagation is extended. The Frobenius and the Krein-Heinz-Rellich factorization theorems and the Etgen Pawlowski oscillation criterion are generalized for equations of any order with operator-valued coefficients. Brusentsev's recent example of a two term fourth order differential operator with deficiency index 4 is discussed.