A density problem for orthogonal rational functions

Let {αn}n=1∞ be a sequence of points in the open unit disk in the complex plane and letB0=1 and Bn(z)=∏k=0nαk|αk|αk−z1−αkz, n=1,2,…,(αk/|αk|=−1 when αk=0). We putL=span{Bn: n=0,1,2,…}and we consider the following ‘moment’ problem: a positive-definite Hermitian inner product 〈·,·〉 on L×L, find a nondecreasing function μ on [−π,π] (or a positive Borel measure μ on [−π,π)) such that〈f,g〉=∫−ππf(eiθ)g(eiθ) dμ(θ) for f, g∈L.We give a necessary and sufficient condition (called ‘N-extremality’) on a solution μ of the moment problem in order that L is dense in L2μ.