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SUMMARY:Paata Ivanisvili (University of California Irvine)
DTSTART:20250211T210000Z
DTEND:20250211T220000Z
DTSTAMP:20260423T024552Z
UID:OARS/66
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OARS/66/">Ja
 ckson's inequality on the hypercube</a>\nby Paata Ivanisvili (University o
 f California Irvine) as part of OARS Online Analysis Research Seminar\n\n\
 nAbstract\nI will talk about the uniform polynomial approximation problem 
 on the hypercube of dimension $n$. I will present two results\, first indi
 cating that there is a threshold power $n/2$\, i.e.\, polynomials of degre
 e at most $0.4999n$ will not always approximate well enough functions of c
 onstant sensitivity. The second result\, on the opposite side\, gives quan
 titative estimates on the error of approximation when  degree is close to 
 $n$. There will be two applications presented: one showing that sensitivit
 y theorem does not hold for bounded real valued functions when degree is r
 eplaced by approximate degree. The second application will be a counterexa
 mple to reverse Markov-Bernstein inequality  for functions in $L^1$ tail s
 pace having frequencies at least $0.4999n$. This is joint work with Roman 
 Vershynin and Xinyuan Xie.\n
LOCATION:https://researchseminars.org/talk/OARS/66/
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