An addendum to Krein's formula
Some former results of Sh. N. Saakjan concerning Krein's formula for the resolvent difference of two selfadjoint extensions \(A_1\) and \(A_2\) of a densely defined closed symmetric operator \(\dot A\) with equal defect numbers are discussed and supplemented. To each selfadjoint extension \(A\) of \(\dot A\) and a subspace \(N\subset N_+= \text{ker}(\dot A^*- i)\) the Weyl-Titchmarsh operator-valued function \(M_{A,N}(z)\), \(z\in\rho(A)\), is corresponding. The linear fractional transformation relating the Weyl-Titchmarsh operators \(M_{A_1,N_+}\) and \(M_{A_2,N_+}\) is derived.
resolvent difference of two selfadjoint extensions
densely defined closed symmetric operator
Weyl-Titchmarsh operator-valued function
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