Matrix Transformations and Disk of Convergence in Interpolation Processes

Abstract EN

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.