Interpolation of data by smooth nonnegative functions

DOI10.4171/RMI/938zbMath1366.65010arXiv1603.02330MaRDI QIDQ520724

Arie Israel, Garving K. Luli, Charles L. Fefferman

Publication date: 5 April 2017

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

Full work available at URL: https://arxiv.org/abs/1603.02330

zbMATH Keywords

Whitney extension problemconstrained interpolation\(n\)-dimensional real spacenonnegative interpolation

Mathematics Subject Classification ID

Numerical interpolation (65D05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05)

Related Items (16)

Locally \(C^{1,1}\) convex extensions of \(1\)-jets ⋮ Global geometry and \(C^1\) convex extensions of 1-jets ⋮ Sharp finiteness principles for Lipschitz selections ⋮ Finiteness principles for smooth selection ⋮ Explicit formulas for 𝐶^{1,1} Glaeser-Whitney extensions of 1-Taylor fields in Hilbert spaces ⋮ \(C^m\) semialgebraic sections over the plane ⋮ Smooth selection for infinite sets ⋮ Whitney's extension theorem and the finiteness principle for curves in the Heisenberg group ⋮ Univariate range-restricted \(C^2\) interpolation algorithms ⋮ Explicit formulas for \(C^{1,1}\) and \(C_{\operatorname{conv}}^{1, \omega}\) extensions of 1-jets in Hilbert and superreflexive spaces ⋮ Nonnegative \(\mathrm C^2(\mathbb R^2)\) interpolation ⋮ \(C^2(\mathbb{R}^2)\) nonnegative extension by bounded-depth operators ⋮ Prescribing tangent hyperplanes to $C^{1,1}$ and $C^{1,\omega}$ convex hypersurfaces in Hilbert and superreflexive Banach spaces ⋮ Algorithms for nonnegative \(\mathrm{C}^2(\mathbb R^2)\) interpolation ⋮ \(C^{1, \omega }\) extension formulas for $1$-jets on Hilbert spaces ⋮ Min-max formulas for nonlocal elliptic operators

Cites Work

• Whitney's extension problem for \(C^m\)
• Higher-order tangents and Fefferman's paper on Whitney's extension problem
• The Whitney problem of existence of a linear extension operator
• Differentiable functions defined in closed sets. A problem of Whitney
• A sharp form of Whitney's extension theorem
• \(C^m\) extension by linear operators
• A generalized sharp Whitney theorem for jets
• Whitney’s extension problem for multivariate 𝐶^{1,𝜔}-functions
• Whitney’s extension problems and interpolation of data
• The trace of jet space 𝐽^{𝑘}Λ^{𝜔} to an arbitrary closed subset of ℝⁿ
• Unnamed Item

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