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.


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