020 Catherine Bénéteau

Catherine Bénéteau (University of South Florida, USA) // A survey of optimal polynomial approximants and connections to digital filters // In this talk, I will discuss the notion of optimal polynomial approximants, which are polynomials that approximate, in some sense, inverses of functions in certain Hilbert spaces of analytic functions. In the last 10 years, a number of papers have appeared examining the zeros of these polynomials, rates of convergence, efficient algorithms for their computation, and connections to orthogonal polynomials and reproducing kernels, among other topics. On the other hand, in the 70s, researchers in engineering and applied mathematics introduced least squares inverses in the context of digital filters in signal processing. It turns out that in the Hardy space $H^2$ the optimal polynomial approximants and the least squares inverses are identical. In this talk, I will survey results related to the zeros of optimal polynomial approximants and implications