On the Whitney distortion extension problem for $C^m(\mathbb R^n)$ and $C^{\infty}(\mathbb R^n)$ and its applications to interpolation and alignment of data in $\mathbb R^n$

Steven B. Damelin, Charles Fefferman

Type: Preprint

Publication Date: 2015-01-01

Citations: 2

DOI: https://doi.org/10.48550/arxiv.1505.06950

View Publication

Locations

arXiv (Cornell University) - View
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	On Whitney Extensions of almost isometries with small distortion, Interpolation and Alignment in $\Bbb R^D$	2014	Charles Fefferman Steven B. Damelin
+	On Smooth Whitney Extensions of almost isometries with small distortion, Interpolation and Alignment in $\Bbb R^D$-Part 1	2014	Steven B. Damelin Charles Fefferman
+	On the Whitney Extension-Interpolation-Alignment problem for almost isometries with small distortion in $\Bbb R^D$	2014	Steven B. Damelin Charles Fefferman
+	On Distorted Smooth Extensions, Euclidean Motions and Alignment and Interpolation of Data in $\mathbb R^D$ II	2014	Charles Fefferman Steven B. Damelin
+	On Euclidean Motions, Distorted Smooth Extensions, Alignment and Interpolation of Data in $\Bbb R^D$	2014	Charles Fefferman Steven B. Damelin
+	On Extensions of e Diffeomorphisms	2015	Steven B. Damelin Charles Fefferman
+	Extensions of Smooth Small Distortions [41]: Introduction	2024
+	Extensions in $\mathbb R^D$	2014	Steven B. Damelin Charles Fefferman
+	Whitney extensions and orthonormal expansions	2023	S. B. Damelin
+	Extensions of Smooth Small Distortions: Cubes, Partitions of Unity, Whitney Machinery	2024
+	Extensions, interpolation and matching in $R^D$	2014	Steven B. Damelin Charles Fefferman
+	The Proof of Theorem 2.3	2024
+	Two-point distortion bounds for biholomorphic mappings of the ball in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">C</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>	2014	Jerry R. Muir
+	Mappings of preserving $n$-distance one in $n$-normed spaces	2016	Xujian Huang Dongni Tan
+ PDF Chat	Union of Euclidean Metric Spaces is Euclidean	2016	Konstantin Makarychev Yury Makarychev
+ PDF Chat	On the Whitney extension problem for near isometries and beyond	2021	Steven B. Damelin
+	On the Whitney extension problem for near isometries and beyond.	2021	Steven B. Damelin
+	Quantitative localization and comparison of invariant distances of domains in $\mathbb C^n$	2021	Nikolai Nikolov Pascal J. Thomas
+ PDF Chat	Quantitative Localization and Comparison of Invariant Distances of Domains in $$\mathbb C^n$$	2022	Николай Николов Pascal J. Thomas
+	On isometries of the Kobayashi and Carathéodory metrics	2010	Prachi Mahajan

Works That Cite This (2)

Action	Title	Year	Authors
+	On the extension of quasisymmetric maps	2016	Pekka Alestalo D. A. Trotsenko
+ PDF Chat	On Surface Completion and Image Inpainting by Biharmonic Functions: Numerical Aspects	2018	Steven B. Damelin N. S. Hoang

Works Cited by This (31)

Action	Title	Year	Authors
+	Embeddings and Extensions in Analysis	1975	J. H. Wells L. R. Williams
+	Minimal Lipschitz Extensions to Differentiable Functions Defined on a Hilbert Space	2009	Erwan Le Gruyer
+	Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Freud Weights	1995	D. S. Lubinsky D.M. Matjila
+ PDF Chat	Interpolation and extrapolation of smooth functions by linear operators	2005	Charles Fefferman
+ PDF Chat	Mean Convergence of Lagrange Interpolation for Exponential weights on [-1, 1]	1998	D. S. Lubinsky
+ PDF Chat	An example related to Whitney extension with almost minimal $C^m$ norm	2009	Charles Fefferman Bo’az Klartag
+	The Whitney problem of existence of a linear extension operator	1997	Yuri Brudnyi Pavel Shvartsman
+	Analytic Extensions of Differentiable Functions Defined in Closed Sets	1992	Hassler Whitney
+	Generalized procrustes analysis	1975	J. C. Gower
+ PDF Chat	C<sup>m</sup>extension by linear operators	2007	Charles Fefferman