Approximation by analytic matrix functions. The four block problem

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dc.creatorPeller, Vladimir
dc.creatorTreil, Sergei
dc.date1995-12-22
dc.date.accessioned2026-07-07T09:15:25Z
dc.date.available2026-07-07T09:15:25Z
dc.descriptionWe study the problem of finding a superoptimal solution to the four block problem. Given a bounded block matrix function $\left(\begin{array}{cc}Φ_{11} &Φ_{12}\\Φ_{21}&Φ_{22}\end{array}\right)$ on the unit circle the four block problem is to minimize the $L^\infty$ norm of $\left(\begin{array}{cc} Φ_{11}-F&Φ_{12}\\Φ_{21}&Φ_{22}\end{array}\right)$ over $F\in H^\infty$. Such a minimizing $F$ (an optimal solution) is almost never unique. We consider the problem to find a superoptimal solution which minimizes not only the supremum of the matrix norms but also the suprema of all further singular values. We give a natural condition under which the superoptimal solution is unique.
dc.identifierhttps://arxiv.org/abs/math/9512223
dc.identifierhttp://arxiv.org/abs/math/9512223
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153014
dc.subjectClassical Analysis and ODEs
dc.titleApproximation by analytic matrix functions. The four block problem
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