Doctoral dissertation

General Framework

The Bernstein Markov Property (BMP) is an asymptotic growth assumption on the ratios of maximum and L^2 norms of polynomials (or other nested families of functions). Such a property is the core of my research, being the link between different areas of Mathematics as Complex Analysis, (Pluri-)Potential Theory and Approximation Theory.
Admissible meshes (AM) are sequences of sampling sets for polynomials for whose cardinality slowly increases with respect to the considered degree and for which a sampling inequality holds. AM constitute a discrete (computational) counterpart of the Bernstein Markov measures and enjoy much of their properties, e.g., the L^2 methods based on BMP can be computed on admissible meshes, we build algorithms based on this.