Abstract
In this note we show that theH 2 optimization of theH ∞ interpolant in the Carathéodory-Schur problem reduces to a finite dimensional albeit very nonlinear problem. Moreover we prove that theH 2-optimalH ∞ interpolant can be rational only in the trivial case, namely when it coincides with the original given polynomial.
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Foias, C., Frazho, A.E. & Li, W.S. OnH 2 minimization for the Carathéodory-Schur interpolation problem. Integr equ oper theory 21, 24–32 (1995). https://doi.org/10.1007/BF01262990
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DOI: https://doi.org/10.1007/BF01262990