\({\mathcal C}^m\)-norms on finite sets and \({\mathcal C}^m\) extension

DOI10.1215/S0012-7094-07-13711-6zbMath1116.58005OpenAlexW1485553355MaRDI QIDQ877482

Pierre D. Milman, Edward Bierstone

Publication date: 23 April 2007

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-07-13711-6

zbMATH Keywords

differentiable functionsextension problemsWhitney jetsparatangent spaces

Mathematics Subject Classification ID

Jets in global analysis (58A20) Continuity and differentiation questions (26B05) Special properties of functions of several variables, Hölder conditions, etc. (26B35) Differentiable maps on manifolds (58C25)

Related Items (13)

Finiteness principles for smooth selection ⋮ Fitting a \(C^m\)-smooth function to data. III. ⋮ \(C^2\) interpolation with range restriction ⋮ Sobolev \(L_p^2\)-functions on closed subsets of \(\mathbb R^2\) ⋮ The Whitney extension problem and Lipschitz selections of set-valued mappings in jet-spaces ⋮ The Brenner-Hochster-Kollár and Whitney problems for vector-valued functions and jets ⋮ A coordinate-free proof of the finiteness principle for Whitney's extension problem ⋮ On properties of geometric preduals of \({\mathrm C^{k,\omega}}\) spaces ⋮ Algorithms for nonnegative \(\mathrm{C}^2(\mathbb R^2)\) interpolation ⋮ Efficient algorithms for approximate smooth selection ⋮ Differential calculus on topological spaces with weak Markov structure. I ⋮ Traces of $C^{k}$ functions on weak Markov subsets of $\mathbb R^{n}$ ⋮ The norm of linear extension operators for \(C^{m-1,1}(\mathbb{R}^n)\)

Cites Work

• Unnamed Item
• Étude de quelques algèbres tayloriennes
• Whitney's extension problem for \(C^m\)
• Higher-order tangents and Fefferman's paper on Whitney's extension problem
• Examples concerning Whitney's \({\mathcal C}^m\) extension problem
• Differentiable functions defined in closed sets. A problem of Whitney
• A sharp form of Whitney's extension theorem
• \(C^1\) extensions of functions and stabilization of Glaeser refinements
• Whitney’s extension problem for multivariate 𝐶^{1,𝜔}-functions
• The Whitney extension problem and Lipschitz selections of set-valued mappings in jet-spaces
• Differentiable Functions Defined in Closed Sets. I

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