On closed Hermitian operators and their selfadjoint extensions

The paper deals with closed Hermitian operators and their selfadjoint extensions. New criteria are obtained for Hermitian operators to be regular in the sense of M. A. Krasnosel'skii. For arbitrary closed Hermitian operators an expression is found for the extent to which an extended generalized resolvent fails to be an $R$-function. A new class of operators is found and investigated for which $(\widehat R_\lambda u,u)$ is an $R$-function for all admissible elements $u$.
Bibliography: 14 titles.