Interpolation and extrapolation of smooth functions by linear operators

DOI10.4171/RMI/424zbMath1084.58003OpenAlexW1985938387MaRDI QIDQ2567450

Charles L. Fefferman

Publication date: 5 October 2005

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/39750

zbMATH Keywords

differentiable functionslinear extension operatorsWhitney type theorems

Mathematics Subject Classification ID

(C^infty)-functions, quasi-analytic functions (26E10) Helly-type theorems and geometric transversal theory (52A35) Differentiable maps on manifolds (58C25)

Related Items (27)

Fitting a \(C^m\)-smooth function to data. III. ⋮ A bounded linear extension operator for \(L^{2,p}(\mathbb R^2)\) ⋮ \(C^m\) semialgebraic sections over the plane ⋮ Smooth selection for infinite sets ⋮ The \(C^m\) norm of a function with prescribed jets. I. ⋮ \(C^2\) interpolation with range restriction ⋮ Nonnegative \(\mathrm C^2(\mathbb R^2)\) interpolation ⋮ \(C^2(\mathbb{R}^2)\) nonnegative extension by bounded-depth operators ⋮ 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 ⋮ Extensions and their minimizations on the Sierpinski gasket ⋮ A Hermite extension method for numerical differentiation ⋮ Testing the manifold hypothesis ⋮ \(C^{m,\omega}\) extension by bounded-depth linear operators ⋮ Algorithms for nonnegative \(\mathrm{C}^2(\mathbb R^2)\) interpolation ⋮ The structure of linear extension operators for \(C^m\) ⋮ An example related to Whitney extension with almost minimal \(C^m\) norm ⋮ Whitney’s extension problems and interpolation of data ⋮ Efficient algorithms for approximate smooth selection ⋮ On the structure of Lipschitz-free spaces ⋮ Differential calculus on topological spaces with weak Markov structure. I ⋮ Extension of \(C^{m, \omega}\)-smooth functions by linear operators ⋮ Fitting a \(C^m\)-smooth function to data. II ⋮ The \(C^m\) norm of a function with prescribed jets. II ⋮ Traces of $C^{k}$ functions on weak Markov subsets of $\mathbb R^{n}$ ⋮ The norm of linear extension operators for \(C^{m-1,1}(\mathbb{R}^n)\) ⋮ A generalized sharp Whitney theorem for jets

Cites Work

• Unnamed Item
• The Whitney problem of existence of a linear extension operator
• Differentiable functions defined in closed sets. A problem of Whitney
• Whitney’s extension problem for multivariate 𝐶^{1,𝜔}-functions

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