@Article{BCQ2016,
  author = {Baratchart, L. and Chevillard, S. and Qian, T.},
  title =        {{Minimax principle and lower bounds in $H^2$-rational approximation}},
  journal = 	 {{Journal of Approximation Theory}},
  year =         {2016},
  volume = {206},
  pages = {17--47},
  url = {http://dx.doi.org/10.1016/j.jat.2015.03.004},
  abstract = {We derive lower bounds in rational approximation of given degree
                  to functions in the Hardy space $H^2$ of the unit disk. We
                  apply these to asymptotic error rates in rational
                  approximation to Blaschke products and to Cauchy integrals on
                  geodesic arcs. We also explain how to compute such bounds,
                  either using Adamjan-Arov-Krein theory or linearized errors,
                  and we present a couple of numerical experiments. We dwell on
                  a maximin principle developed in the article \emph{An $L^p$
                  analog of AAK theory for $p \ge 2$}, by L. Baratchart and
                  F. Seyfert, in the Journal of Functional Analysis, 191 (1),
                  pp. 52-122, 2012.},
  keywords = {complex rational approximation, Hardy spaces, lower bounds, error
                  rates}
}