A separating problem on function spaces (Q1073965)

This paper is mainly concerned with \(H^{\infty}\)-separating sequences \((z_ n)\). A sequence \((z_ n)\) of points in the open unit disc is called \(H^{\infty}\)-separating if \(\sum | f(z_ n)|\) diverges for every nonzero function \(f\in H^{\infty}\). The authors give necessary and also some sufficient conditions that a sequence is \(H^{\infty}\)-separating. Several examples are presented. At the end of the paper the problem of separating sequences is also studied for other spaces of analytic functions, e.g. the Nevanlinna class and the disc algebra.