Some elementary inequalities, based on the non-elementary notion of Dubiner distance, show that norming sets for multivariate polynomials are stable under small perturbations in such a distance. As a corollary, we get anew result on the stability of Lebesgue constants.
Dubiner distance and stability of Lebesgue constants
Marco Vianello
2019
Abstract
Some elementary inequalities, based on the non-elementary notion of Dubiner distance, show that norming sets for multivariate polynomials are stable under small perturbations in such a distance. As a corollary, we get anew result on the stability of Lebesgue constants.
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