Federico Piazzon

Small perturbations of polynomial meshes

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.

Optimal polynomial admissible meshes on some classes of compact subsets of R d

We show that any compact subset of R d which is the closure of a bounded star-shaped Lipschitz domain � , such that � � has positive reach in the sense of Federer, admits an optimal AM (admissible mesh), that is a sequence of polynomial norming sets with optimal cardinality. This extends a recent result of A. Kroo on C 2 star-shaped domains.Moreover, we prove constructively the existence of an optimal AM for any K : = � � � R d where � is a bounded C 1 , 1 domain. This is done by a particular multivariate sharp version of the Bernstein Inequality via the distance function.

A note on total degree polynomial optimization by Chebyshev grids

Using the approximation theory notions of polynomial mesh and Dubiner distance in a compact set, we derive error estimates for total degree polynomial optimization on Chebyshev grids of the hypercube.

Some Results on the Rational Bernstein Markov Property in the Complex Plane

The Bernstein–Markov property is an asymptotic quantitative assumption on the growth of uniform norms of polynomials or rational functions on a compact set with respect to

Analytic transformations of admisible meshes

L^2_\mu

Constructing optimal polynomial meshes on planar starlike domains

Lμ2-norms, where

Caratheodory-Tchakaloff Subsampling

\mu