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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 5
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Articles

Small perturbations of polynomial meshes

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Pages 1063-1073 | Received 24 Apr 2011, Accepted 11 Dec 2011, Published online: 18 Jan 2012
 

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.

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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.

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