期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2008
卷号：2008
DOI：10.1155/2008/905635
出版社：Hindawi Publishing Corporation
摘要：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.
