November 2023
Intermediate to advanced
192 pages
3h 29m
English
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.
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 ...