TY - JOUR AU - Chalendar, Isabelle AU - Gorkin, Pamela AU - Partington, Jonathan R. PY - 2010/12/01 Y2 - 2024/03/29 TI - Boundary interpolation and approximation by infinite Blaschke products JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 107 IS - 2 SE - Articles DO - 10.7146/math.scand.a-15157 UR - https://www.mscand.dk/article/view/15157 SP - 305-319 AB - 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 $H^\infty(\Omega)$ where $\Omega$ 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. ER -