Equidistribution of zeros of some polynomials related to cyclic functions

Abstract

In the study of the cyclicity of a function f in reproducing kernel Hilbert spaces an important role is played by sequences of polynomials {p_n}_{nin mathbb {N}} called optimal polynomial approximants (o.p.a.). For many such spaces and when the functions f generating those o.p.a. are polynomials without zeros inside the disk but with some zeros on its boundary, we find that the weakly asympotic distribution of the zeros of 1-p_nf is the uniform measure on the unit circle.