Widths and optimal sampling in spaces of analytic functions (Q1357538)

Let \(\Omega\) be a finitely-connected domain in the complex plane and let \(\mu\) be a positive measure on \(\Omega\) with compact support \(E\) within \(\Omega\). Let \(A_p\) be the restriction to \(E\) of the closed unit ball of the Hardy space \(H^p (\Omega)\). The main result of the paper is that the Kolmogorov, Gelfand and linear \(n\)-widths of \(A_p\) in \(L^q (\mu)\) are comparable in size to each other and to the sampling error if \(q\leq p\). Moreover, if \(p= q=2\) and \(E\) is small enough, then it is shown that all these quantities are equal.