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On positive differential operators (deficiency indices, factorization, perturbations)

Published online by Cambridge University Press:  14 November 2011

F. S. Rofe-Beketov
F. S. Rofe-Beketov
Affiliation:
Physico-Technical Institute of Low Temperatures, Ukr.S.S.R. Academy of Sciences, Kharkov, U.S.S.R.
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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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 247 - 257
Copyright
Copyright © Royal Society of Edinburgh 1984

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