The abstract interpolation problem (AIP) in the Schur class was posed
by V. Katznelson, A. Kheifets, and P. Yuditskii in 1987. In the present paper we
consider an analog of AIP for the generalized Nevanlinna class $N_κ(L)$ in the nondegenerate
case. We associate with the data set of the AIP a symmetric linear relation $\hat A$ acting in a Pontryagin space. The description of all solutions of the AIP
is reduced to the problem of description of all $L$-resolvents of this symmetric linear
relation $\hat A$. The latter set is parametrized by application of the indefinite version
of Kreın’s representation theory for symmetric linear relations in Pontryagin spaces
developed by M. G. Kreın and H. Langer in [22] and a formula for the $L$-resolvent
matrix obtained by V. Derkach and M. Malamud in [11].
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Title
Abstract interpolation problem in generalized Nevanlinna classes