On the Whitney Extension-Interpolation-Alignment problem for almost isometries with small distortion in ${\mathbb{R}}^D$

Abstract

In this paper, we study the following problem. Let $D\ge 2$, $S\subset {\mathbb{R}}^D$ be finite and let $\varphi :S\to {\mathbb{R}}^D$ with $\varphi$ a small distortion on $S$. We solve the Whitney extension-interpolation-alignment problem of how to understand when $\varphi$ can be extended to a function $\Phi :{\mathbb{R}}^D\to {\mathbb{R}}^D$ which is a smooth small distortion on ${\mathbb{R}}^D$. The work in this paper appears in the research memoir [14]

The material for this paper appears in the research memoir: S. B. Damelin, Near extensions and Alignment of data in ${\mathbb{R}}^n$: Whitney extensions of smooth near isometries, shortest paths, equidistribution, clustering and non-rigid alignment of data in Euclidean space, John Wiley & Sons, November 2023

References in corpus (2)

• Cramér-Rao bounds for synchronization of rotations
• Fourier-Bessel rotational invariant eigenimages