Near Extensions and Alignment of Data in R(superscript)n

1 Variants 1–2

In this chapter, we introduce the classical Whitney extension problem. Thereafter, we introduce the near distorted Whitney extension problem and two variants of it. The first, via a purely harmonic analysis problem and the second, translated into a problem related to non-rigid alignment and interpolation of data in . We discuss the Procrustes rigid alignment problem.

1.1 The Whitney Extension Problem

Given a real valued function on an arbitrary compact set in , the classical Whitney extension problem asks how can one decide whether extends to a function in , the space of real valued functions on whose derivatives of order are continuous and bounded? Whitney [114, 115 ...