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On two-sided interpolation for upper triangular matrices. (English) Zbl 1015.47009

Summary: The space of upper triangular matrices with Hilbert–Schmidt norm can be viewed as a finite dimensional analogue of the Hardy space \(\mathbf H_2\) of the unit disk when one introduces the adequate notion of “point” evaluation. A bitangential interpolation problem in this setting is studied. The description of all solutions in terms of the Beurling-Lax representation is given.

MSC:

47A57 Linear operator methods in interpolation, moment and extension problems
47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.
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