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SUMMARY:Catherine Bénéteau (University of South Florida)
DTSTART:20201027T130000Z
DTEND:20201027T140000Z
DTSTAMP:20260422T201706Z
UID:CAvid/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/18/">A
  survey of optimal polynomial approximants and connections to digital filt
 ers</a>\nby Catherine Bénéteau (University of South Florida) as part of 
 CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\
 nIn this talk\, I will discuss the notion of optimal polynomial approximan
 ts\, 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 poly
 nomials\, rates of convergence\, efficient algorithms for their computatio
 n\, and connections to orthogonal polynomials and reproducing kernels\, am
 ong other topics. On the other hand\, in the 70s\, researchers in engineer
 ing and applied mathematics introduced least squares inverses in the conte
 xt of digital filters in signal processing. It turns out that in the Hardy
  space $H^2$ the optimal polynomial approximants and the least squares inv
 erses are identical. In this talk\, I will survey results related to the z
 eros of optimal polynomial approximants and implications for the design of
  ideal digital filters. This talk is based on a preprint of a survey paper
  that is joint with Ray Centner.\n
LOCATION:https://researchseminars.org/talk/CAvid/18/
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