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Computational Methods and Function Theory

, Volume 15, Issue 3, pp 403–425 | Cite as

On Configurations of Points on the Sphere and Applications to Approximation of Holomorphic Functions by Lagrange Interpolants

  • Phung Van Manh
Article
  • 53 Downloads

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.

Keywords

Lagrange interpolation Chung–Yao lattices Configurations on spheres 

Mathematics Subject Classification

Primary 41A05 41A63 52C35 

Notes

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationHanoiVietnam

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