We prove the computability of a version of Whitney Extension, when the input is suitably represented. More specifically, if F⊆Rn is a closed set represented so that the distance function x↦d(x,F) can be computed, and (f(k¯))|k¯|≤m is a Whitney jet of order m on F, then we can compute g∈Cm(Rn) such that g and its partial derivatives coincide on F with the corresponding functions of (f(k¯))|k¯|≤m.
Computability of a whitney extension
Marcone A.Membro del Collaboration Group
2026-01-01
Abstract
We prove the computability of a version of Whitney Extension, when the input is suitably represented. More specifically, if F⊆Rn is a closed set represented so that the distance function x↦d(x,F) can be computed, and (f(k¯))|k¯|≤m is a Whitney jet of order m on F, then we can compute g∈Cm(Rn) such that g and its partial derivatives coincide on F with the corresponding functions of (f(k¯))|k¯|≤m.File in questo prodotto:
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