On properties of (trigonometric) polynomials

Vendredi 6 mars 11:00-12:00 - Daniel Perez - Université Paris-sud

Résumé : The study of trigonometric polynomials is one with a rich history. In this talk, we will mostly concern ourselves with the roots of such polynomials of fixed degree n and in particular, we will give an explicit algorithm to find these roots. In order to achieve this, we will explore the theory of equirepartition of roots of ordinary polynomials by Erdős and Turán with a bit of potential. In a subsequent part of the talk, we will examine the properties of trigonometric polynomials in the probabilistic setting and give some interesting results concerning the properties of these objects (expected number of zeros, law of suprema, limiting objects when they exist...).

Lieu : Salle 3L15 - Institut de mathtématiques d’Orsay

On properties of (trigonometric) polynomials  Version PDF