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

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

by Steven B. Damelin
November 2023
Intermediate to advanced content levelIntermediate to advanced
192 pages
3h 29m
English
Wiley
Content preview from 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 double-struck upper R Superscript d. We discuss the Procrustes rigid alignment problem.

1.1 The Whitney Extension Problem

Given a real valued function phi on an arbitrary compact set in double-struck upper R Superscript n, the classical Whitney extension problem asks how can one decide whether phi extends to a function normal upper Phi in upper C Superscript m Baseline left-parenthesis double-struck upper R Superscript n Baseline right-parenthesis comma m greater-than-or-equal-to 1, the space of real valued functions on double-struck upper R Superscript n whose derivatives of order m are continuous and bounded? Whitney [114, 115 ...

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Publisher Resources

ISBN: 9781394196777Purchase Link