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arXiv · 1804.08498

All solutions to an operator Nevanlinna-Pick interpolation problem

A. E. Frazho·S. Ter Horst·M. A. Kaashoek
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Abstract

The main results presented in this paper provide a complete and explicit description of all solutions to the left tangential operator Nevanlinna- Pick interpolation problem assuming the associated Pick operator is strictly positive. The complexity of the solutions is similar to that found in descriptions of the sub-optimal Nehari problem and variation on the Nevanlinna-Pick interpolation problem in the Wiener class that have been obtained through the band method. The main techniques used to derive the formulas are based on the theory of co-isometric realizations, and use the Douglas factorization lemma and state space calculations. A new feature is that we do not assume an additional stability assumption on our data, which allows us to view the Leech problem and a large class of commutant lifting problems as special cases. Although the paper has partly the character of a survey article, all results are proved in detail and some background material has been added to make the paper accessible to a large audience including engineers.

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A. E. Frazho, S. Ter Horst, M. A. Kaashoek. 2018-04-23. All solutions to an operator Nevanlinna-Pick interpolation problem. https://doi.org/10.1007/978-3-319-62527-0_5

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