On the recovery of functions from pointwise boundary values in a Hardy-Sobolev class of the disk

AbstractThis paper deals with a particular problem in convergent interpolation to analytic functions from boundary values. We first stress some system-theoretic motivations for these questions. Then, a linear triangular interpolation scheme for analytic functions in the Hardy-Sobolev class D2 of the disk is studied, when the interpolation points lie on the boundary circle. Specifically, the sequence of interpolating functions of minimum norm is shown to converge to the original function, provided the closure of the interpolation set has positive measure on the circle. This induces uniform convergence in the sense of the usual Hardy norms which is further estimated from above and from below in the particular case where the interpolation points are dense in some subarc of the circle