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Results in Mathematics

, Volume 11, Issue 1–2, pp 144–164 | Cite as

Interpolation on the sphere and bounds for the Lagrangian square sums

  • M. Reimer
Article

Summary

For spaces of polynomial functions on the sphere which are invariant against rotation, the square-sums of the Lagrangians can be estimated by means of the smallest eigenvalue of a positive definite system matrix defined by the reproducing kernel and the nodes used. As a consequence, bounds for the corresponding Lebesgueconstants are obtained. There are examples where the method leads to an estimation of the square-sum by one, which cannot be improved. In this case the Lagrangians perform an extremal basis.

Keywords

Fundamental System Interpolation Operator Nodal System Lebesgue Constant Regular Polyhedron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Birkhäuser Verlag, Basel 1987

Authors and Affiliations

  • M. Reimer
    • 1
  1. 1.Lehrstuhl Mathematik III Fachbereich MathematikUniversität DortmundDortmund 50

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