be a closed symmetric operator of defect one in a Krein space
and assume that
possesses a self-adjoint extension in
which locally has the same spectral properties as a definitizable operator. We show that the Krein-Naimark formula establishes a bijective correspondence between the compressed resolvents of locally definitizable self-adjoint extensions
acting in Krein spaces
K x H
and a special subclass of meromorphic functions.