Hankel Operators and the Nehari Problem

The Nehari problem is naturally formulated in frequency-domain terms: given a matrix-valued function $$G \in {L_\infty }(( - J\infty ,J\infty );{\mathbb{C}^{kxm}})$$, find the distance of G from the antistable matrix-valued functions K such that $$K( - s) \in {H_\infty }({C^{kxm}});$$; that is, find $$\begin{array}{*{20}{c}}{\inf } \\{K\left( { - s} \right) \in {H_\infty }\left( {{C^{kxm}}} \right)}\end{array}\begin{array}{*{20}{c}}{{{\left\| {G + K} \right\|}_\infty }: = } \\{}\end{array}\begin{array}{*{20}{c}}{\inf } \\ {K\left( { - s} \right) \in {H_\infty }\left( {{C^{kxm}}} \right)}\end{array}\begin{array}{*{20}{c}}{ess{\text{ sup}}} \\{\omega \in R}\end{array}\begin{array}{*{20}{c}}{\left\| {G\left( {jw} \right) + K\left( {j\omega } \right)} \right\|.} \\{}\end{array}$$