A bang-bang theorem for optimization over spaces of analytic functions (Q1074100)

Let D be the unit disk in the complex plane, \(\Pi\) its boundary, \(H^{\infty}(N)\) the space of boundary values of N-tuples of bounded holomorphic functions on D. Let \(\Gamma\) be a real-valued function on \(\Pi\) \(\times C\), and consider the problem of finding the \(\inf_ h\| \Gamma (\cdot,h)\|_{\infty}\). This paper considers qualitative properties of the optimizing function for this problem, which has interest in several fields of electrical engineering, such as control and frequency-domain synthesis.