28 citations · 62 across the 4 of their papers we have counts for
7 papers
A survey of optimal polynomial approximants, applications to digital filter design, and related open problems
Catherine Bénéteau, Raymond Centner
In the last few years, the notion of optimal polynomial approximant has appeared in the mathematics literature in connection with Hilbert spaces of analytic functions of one or mor…
Boundary behavior of optimal polynomial approximants
Catherine Bénéteau, Myrto Manolaki, Daniel Seco
In this paper, we provide an efficient method for computing the Taylor coefficients of , where denotes the optimal polynomial approximant of degree to in a…
Simultaneous zero-free approximation and universal optimal polynomial approximants
Catherine Bénéteau, Oleg Ivrii, Myrto Manolaki +1
Let be a closed subset of the unit circle of measure zero. Recently, Beise and Müller showed the existence of a function in the Hardy space for which the partial sums of…
Remarks on Inner Functions and Optimal Approximants
Catherine Bénéteau, Matthew Fleeman, Dmitry Khavinson +2
We discuss the concept of inner function in reproducing kernel Hilbert spaces with an orthogonal basis of monomials and examine connections between inner functions and optimal poly…
Zeros of optimal polynomial approximants: Jacobi matrices and Jentzsch-type theorems
Catherine Bénéteau, Dmitry Khavinson, Constanze Liaw +2
We study the structure of the zeros of optimal polynomial approximants to reciprocals of functions in Hilbert spaces of analytic functions in the unit disk. In many instances, we f…
Cyclic polynomials in two variables
Catherine Bénéteau, Greg Knese, Łukasz Kosiński +3
We give a complete characterization of polynomials in two complex variables that are cyclic with respect to the coordinate shifts acting on Dirichlet-type spaces in the bidisk, whi…
Cyclicity in Dirichlet-type spaces and extremal polynomials II: functions on the bidisk
Catherine Bénéteau, Alberto A. Condori, Constanze Liaw +2
We study Dirichlet-type spaces of analytic functions in the unit bidisk and their cyclic elements. These are the functions for which there exists a sequence $(…