Nevanlinna type families of linear relations and the dilation theorem - Mogilevskii, V. I. (Methods of Functional Analysis and Topology, 2006)
Let H1 be a subspace in a Hilbert space H0 and let C(H_0,H_1) be the set of all closed linear relations from H_0 to H_1. We introduce a Nevanlinna type class R_+ (H_0,H_1) of holomorphic functions with values in C(H_0,H_1) and investigate its properties. In particular we prove the existence of a dilation for every function τ_+(·)R_+ (H_0,H_1). In what follows these results will be used for the derivation of the Krein type formula for generalized resolvents of a symmetric operator with arbitrary (not necessarily equal) deficiency indices.