The Krein formula for generalized resolvents in degenerated inner product spaces

Let S be a symmetric operator with defect index (1,1) in a Pontryagin space H. The Krein formula establishes a bijective correspondence between the ge neralized resolvents of S and the set of Nevanlinna functions as parameters . We give an analogue of the Krein formula in the case that H is a degenera ted inner product space. The set of parameters is determined by a kernel co ndition. These results are applied to some classical interpolation problems with singular data.