Equidistribution of zeros of some polynomials related to cyclic functions

In the study of the cyclicity of a function f in reproducing kernel Hilbert spaces an important role is played by sequences of polynomials 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 polynomials is the uniform measure on the unit circle.

Equidistribution of zeros of some polynomials related to cyclic functions Articles