We prove the computability of a version of Whitney Extension, when the input is suitably represented. More specifically, if F ⊆ R^n 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 ∈ C^m(R^n) such that g and its partial derivatives coincide on F with the corresponding functions of ( f ( ¯ k))_| ¯ k|≤m.
Brun, A., Gherardi, G., Marcone, A. (2026). Computability of a Whitney extension. ARCHIVE FOR MATHEMATICAL LOGIC, On line first, 1-42 [10.1007/s00153-026-01020-8].
Computability of a Whitney extension
Guido Gherardi
;Alberto Marcone
2026
Abstract
We prove the computability of a version of Whitney Extension, when the input is suitably represented. More specifically, if F ⊆ R^n 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 ∈ C^m(R^n) 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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