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Remarks on interpolation in reproducing kernel Hilbert spaces. (English) Zbl 1067.46035

Authors’ abstract: An interpolation problem in reproducing kernel Hilbert spaces is formulated and solved in terms of the minimal solution and the elements of an auxiliary reproducing kernel Hilbert space, subject to a norm constraint. The scheme is illustrated with two particular reproducing kernel Hilbert spaces: the Arveson space and the Bergman space, where the general theorem leads to convenient parametrizations of the solution sets.

MSC:

46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
41A05 Interpolation in approximation theory
47A57 Linear operator methods in interpolation, moment and extension problems
30E99 Miscellaneous topics of analysis in the complex plane
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