A Nonnegative Version of Whitney's Extension Problem

Kevin O'Neill (UC Davis)

16-Nov-2020, 22:00-23:00 (3 years ago)

Abstract: Whitney'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∈ Cᵐ(ℝⁿ) such that f is the restriction of F to E? The classical Whitney 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 question 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.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic


OARS Online Analysis Research Seminar

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Organizers: Rachel Greenfeld*, Zane Li*, Joris Roos*, Ziming Shi
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