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Reproducing kernel Pontryagin spaces. (English) Zbl 0992.46019
Axler, Sheldon (ed.) et al., Holomorphic spaces. Cambridge: Cambridge University Press. Math. Sci. Res. Inst. Publ. 33, 425-444 (1998).
Summary: The theory of reproducing-kernel Pontryagin spaces is surveyed. A new proof is given of an abstract theorem that constructs contraction operators on Pontryagin spaces from densely defined relations. The theory is illustrated with examples from the theory of generalized Schur functions. For the entire collection see [Zbl 0893.00015].
46E22Hilbert spaces with reproducing kernels
46C20Spaces with indefinite inner product
47B50Operators on spaces with an indefinite metric
47A57Operator methods in interpolation, moment and extension problems
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