@article{9fdbd3a2583b4dd581e16d273be59fcd,
title = "Simultaneous zero-free approximation and universal optimal polynomial approximants",
abstract = "Let E be a closed subset of the unit circle of measure zero. Recently, Beise and M{\"u}ller showed the existence of a function in the Hardy space H2 for which the partial sums of its Taylor series approximate any continuous function on E. In this paper, we establish an analogue of this result in a non-linear setting where we consider optimal polynomial approximants of reciprocals of functions in H2 instead of Taylor polynomials. The proof uses a new result on simultaneous zero-free approximation of independent interest. Our results extend to the Dirichlet space D and are expected for more general Dirichlet-type spaces.",
keywords = "Hardy spaces, Optimal polynomial approximants, Universality, Zero-free approximation",
author = "Catherine B{\'e}n{\'e}teau and Oleg Ivrii and Myrto Manolaki and Daniel Seco",
note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",
year = "2020",
month = aug,
doi = "10.1016/j.jat.2020.105389",
language = "אנגלית",
volume = "256",
journal = "Journal of Approximation Theory",
issn = "0021-9045",
publisher = "Academic Press Inc.",
}