## Abstract interpolation problem in generalized Nevanlinna classes.(English)Zbl 1258.47027

The abstract interpolation problem (AIP) for operator-functions in the Schur class was posed by V. Eh. Katsnel’son et al., [Operators in functional spaces and questions of function theory, Collect. Sci. Works, Kiev 1987, 83–96 (1987; Zbl 0703.41005)]. A version of the AIP for the Nevanlinna class was developed by V. Derkach [Operator Theory: Advances and Applications 190, 197–236 (2009; Zbl 1217.47034)]. The author considers an analogue of the AIP for the generalized Nevanlinna class with $$\varkappa <\infty$$ negative squares. The description of all solutions of this AIP is reduced to the description of generalized resolvents of a symmetric linear relation in the Pontryagin space.

### MSC:

 47A57 Linear operator methods in interpolation, moment and extension problems 47B50 Linear operators on spaces with an indefinite metric 47A06 Linear relations (multivalued linear operators) 47A10 Spectrum, resolvent

### Citations:

Zbl 0703.41005; Zbl 1217.47034