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Interpolation problems, extensions of symmetric operators and reproducing kernel spaces. I. (English) Zbl 0737.47016
Topics in matrix and operator theory, Proc. Workshop, Rotterdam/Neth. 1989, Oper. Theory, Adv. Appl. 50, 35-82 (1991).
[For the entire collection see Zbl 0722.00022.]
The aim of the paper is to study interpolation problems for pairs of functions of the extended Nevanlinna class using two different approaches, namely the Krein-Langer theory of extensions of symmetric operators and the de Branges theory of Hilbert spaces of analytic functions, and to make explicit various links between them. (From the authors’ abstract.)
In the first part, some properties of extended Nevanlinna classes in a Hilbert space are studied and the parametrizations of the solutions of the interpolation problem are proved using the Krein-Langer extension theory. Some results pertaining to the Lyapunov equation are presented. In the second part of the paper (to appear), those problems will be treated from the point of view of the de Branges theory.
Reviewer: J.Durdil (Praha)

47A57 Linear operator methods in interpolation, moment and extension problems
47A20 Dilations, extensions, compressions of linear operators
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
40A05 Convergence and divergence of series and sequences