On Krein's Formula in the Case of Non-densely Defined Symmetric Operators

AbstractIn this paper we provide some additional results related to Krein's resolvent formula for a non-densely defined symmetric operator. We show that coefficients in Krein's formula can be expressed in terms of analogues of the classical von Neumann formulas. The relationship between two Weyl–Tichmarsh m-functions corresponding to self-adjoint extensions of a non-densely defined symmetric operator is established