A characterization of the leading coefficient of Nevanlinna's parametrization (Q1320927)

The following condition for an analytic functions \(s:s\) to belongs to the Smirnov class \(N^+\) (in the unit disk \(D\)), \(s^{- 1}\) is a non- extreme point of the unit ball of \(H^\infty\) and the function \(F= (s+ B\overline{E(|s|^2- 1)^{1/2}})^{- 2}\) is an exposed point in \(H^1\), where \(B\) is a Blaschke product with zeros \(\{z_n\}\) and \(E(|s|^2- 1)^{1/2}\) is an outer function with modulus of boundary values \((|s|^2- 1)^{1/2}\), are equivalent to \(s\) being the leading coefficient in the Nevanlinna parametric representation of solutions of a Pick-Nevanlinna problem.