Boundary interpolation and approximation by infinite Blaschke products - Chalendar, Isabelle; Gorkin, Pamela; Partington, Jonathan R. (Mathematica Scandinavica, 2010)
This paper considers the problem of boundary interpolation (in the sense of non-tangential limits) by Blaschke products and interpolating Blaschke products. Simple and constructive proofs, which also work in the more general situation of $H^∞(Ω)$ where $Ω$ is a more general domain, are given of a number of results showing the existence of Blaschke products solving certain interpolation problems at a countable set of points on the circle. A variant of Frostman's theorem is also presented.