Solution to a Bergman space extremal problem for non-vanishing functions
minimize area problems for nonvanishing functions
The author gives an impressive solution to an open problem in function theory. Let \(f(z)= 1+ az+ a_2 z^2+\cdots\) with \(a\geq 0\) be analytic in \(\{|z|< 1\}\). A long standing open problem was to fiind an extremal function solution that minimizes the \(A^2\) norm, and to find, in addition, the exact value of this minimum norm. The author uses his theory of harmonic products as a basic tool. He gives a beautiful solution.
scientific article; zbMATH DE number 6064199