International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 905635, 11 pages
doi:10.1155/2008/905635
Abstract
Let Aρ denote the set of functions analytic in |z|<ρ but not on |z|=ρ (1<ρ<∞). Walsh proved that the difference of the Lagrange polynomial
interpolant of f(z)∈Aρ 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.