Equidistribution of zeros of some polynomials related to cyclic functions

Abstract

AbstractIn the study of the cyclicity of a functionfin reproducing kernel Hilbert spaces an important role is played by sequences of polynomials$$\{p_n\}_{n\in \mathbb {N}}$${pn}n∈Ncalledoptimal polynomial approximants(o.p.a.). For many such spaces and when the functionsfgenerating 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$$1-p_nf$$1-pnfis the uniform measure on the unit circle.