Singular operator as a parameter of self-adjoint extensions

Let A be a symmetric restriction of a self-adjoint bounded from below operator A in a Hilbert space H and let A(infinity) denote the Friedrichs extension of A. We prove that in the case, where A(infinity) not equal A, under natural conditions, each self-adjoint extension ii of A has a unique representation in the form of a generalized sum, (A) over tilde = A (+) over tilde V, where V is a singular operator acting in the A-scale of Hilbert spaces, from H-1(A) to H-1(A). In the particular case, where (A)over dot has deficiency indices (1, 1), this result has been proven by Krein and Yavrian.