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

Neiman, Evgen

Methods Funct. Anal. Topol. 18, No. 3, 266-287 (2012).

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.

Reviewer: Anatoly N. Kochubei (Kyïv)

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

Keywords:

abstract interpolation problem; generalized Nevanlinna classes; generalized resolvents; Pontryagin space

Citations:

Zbl 0703.41005; Zbl 1217.47034