Matrix transformations and disk of convergence in interpolation processes (Q954841)

Summary: Let \(A_{\rho }\) denote the set of functions analytic in \(|z|<\rho \) but not on \(|z|=\rho\) \((1<\rho <\infty )\). Walsh proved that the difference of the Lagrange polynomial interpolant of \(f(z)\in A_{\rho }\) and the partial sum of the Taylor polynomial of \(f\) converges to zero on a larger set than the domain of definition of \(f\). In 1980, Cavaretta et al. have studied the extension of Lagrange interpolation, Hermite interpolation, and Hermite-Birkhoff interpolation processes in a similar manner. In this paper, we apply a certain matrix transformation on the sequences of operators given in the above-mentioned interpolation processes to prove the convergence in larger disks.