The best linear methods and values of widths for some classes of analytic functions in the Bergman weight space (Q378194)

Let \({\mathcal P}_{n-1}\) denote the space of polynomials of degree \(\leq n\). Let \(E(f,{\mathcal P}_{n-1}) = \inf\{\|f-g\|: g \in {\mathcal P}_{n-1}\}\) and for a class \( W^{(r)}_{\Phi,\alpha} (X)\), of analytic functions on the disk, the authors obtain estimates for \(\sup\{E(f,{\mathcal P}_{n-1})\}\) for \(f\) in that class.