Small perturbations of polynomial meshes

Abstract

We show that the property of being a (weakly) admissible mesh for multivariate polynomials is preserved by small perturbations on real and complex Markov compacts. Applications are given to smooth transformations of polynomial meshes and to polynomial interpolation.

Keywords:

• multivariate polynomial inequalities
• (weakly) admissible meshes
• Markov compacts
• multivariate polynomial interpolation

AMS Subject Classifications::

• 30E10
• 41A10
• 41A63
• 65D05

Acknowledgements

The authors thank Len Bos and Jean-Paul Calvi for some helpful discussions and suggestions. This research was supported by the ‘ex-60%’ funds and by the project ‘Interpolation and Extrapolation: new algorithms and applications’ of the University of Padova, and by the INdAM GNCS.