On the hard and soft extensions of a nonnegative operator

In terms of spaces of boundary values, i.e., in a form that, in the case of differential operators, leads immediately to the boundary conditions, we construct the hard and soft extensions of a nonnegative operator in Hilbert space, interpreted as perturbations with a change of the domain of definition of a given positivedefinite operator for which these extensions are assumed known. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 7–9.