Abstract
We find concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size 4 × 4 in the extremal case. Along the way we introduce a new approach that allows us to solve, algorithmically, the contractive completion problem for 4 × 4 Hankel matrices. As an application, we obtain a concrete example of a partially contractive 4 × 4 Hankel matrix, which does not admit a contractive completion.
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