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SUMMARY:Kevin O'Neill (UC Davis)
DTSTART:20201116T220000Z
DTEND:20201116T230000Z
DTSTAMP:20260423T005735Z
UID:OARS/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OARS/7/">A N
 onnegative Version of Whitney's Extension Problem</a>\nby Kevin O'Neill (U
 C Davis) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nW
 hitney's Extension Problem asks the following: Given a compact set E⊂ 
 ℝⁿ and a function f:E→ ℝ\, how can we tell if there exists F∈ C
 ᵐ(ℝⁿ) such that f is the restriction of F to E? The classical Whitne
 y Extension theorem tells us that\, given potential Taylor polynomials Pˣ
  at each x∈E\, there is such an extension F if and only if the Pˣ's are
  compatible under Taylor's theorem. However\, this leaves open the questio
 n of how to tell solely from f. A 2006 paper of Charles Fefferman answers 
 this question. We explain some of the concepts of that paper\, as well as 
 recent work of the speaker\, joint with Fushuai Jiang and Garving K. Luli\
 , which establishes the analogous result when f≥0 and we require F≥0.\
 n
LOCATION:https://researchseminars.org/talk/OARS/7/
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