Constrained Hardy space approximation
This paper establishes the uniqueness of a solution of a minimization problem for continuous functions defined on a subset of the complex unit circle. The author shows, that for each such \(f\), there is a unique function \(h\) -- in the Hardy space \(H^p\) defined on the complex unit circle and which is also subject to the condition that \(|h| < g\) for some positive function \(g\) -- such that \(\|f-h\|\) is minimal. Moreover, this minimal solution can be approximated by smooth functions.
scientific article; zbMATH DE number 5793308