Abstract
We study certain configurations of points on the unit sphere in \(\mathbb {R}^N\). As an application, we prove that the sequence of Lagrange interpolation polynomials of holomorphic functions at certain Chung–Yao lattices converge uniformly to the interpolated functions.
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Acknowledgments
The author wishes to express his thanks to Professor Jean-Paul Calvi for suggesting this problem and for stimulating conversations. The author would like to thank the referees for a careful reading of the manuscript. This work has been partially done during a visit of the author at the Vietnam Institute for Advanced Mathematics in 2014. He wishes to thank this institution for financial support and the warm hospitality that he received there. This work was supported by the NAFOSTED program.
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Communicated by Norman Levenberg.
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Van Manh, P. On Configurations of Points on the Sphere and Applications to Approximation of Holomorphic Functions by Lagrange Interpolants. Comput. Methods Funct. Theory 15, 403–425 (2015). https://doi.org/10.1007/s40315-015-0106-2
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DOI: https://doi.org/10.1007/s40315-015-0106-2