Università degli studi di Padova & Marseille
Date(s) : 14/05/2014 iCal
10 h 00 min - 11 h 00 min
The Bernstein Markov Property (BMP) is a comparability conditions of the Lμ2 and max K|⋅| norms of polynomials for a given a compact set K ⊂ ℂn and a measure μ with supp(μ) ⊆ K. Several variants (i.e., Lp, weighted, …) of this property has been introduced. Bernstein Markov property arises as a key tool in the proofs of some fundamental results in (weighted) Pluripotential theory and random polynomials. More recently, it has been shown that such results can be reinterpreted in a probability fashion proving a Large Deviation Principle. We recall the best-known sufficient condition for the standard BMP and present two new results. Namely, a sufficient mass density condition for the BMP for rational functions and a sufficient mass density condition for the weighted BMP on unbounded closed sets in the complex plane.