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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

10 ε-distorted diffeomorphisms, O(d) and Functions of Bounded Mean Oscillation (BMO)

Up till now, we have spent some time building epsilon-distorted diffeomorphisms from elements of upper S upper O left-parenthesis d right-parenthesis and Euclidean motions. Here epsilon is small enough. In this chapter, [42], we are going to study the following problem, namely, given a epsilon-distorted diffeomorphism, how well can one approximate it by elements of upper O left-parenthesis d right-parenthesis? Here epsilon is small enough. We will study this problem in volume measure.

In studying this problem, we find interesting connections of this problem to the space of functions f : double-struck upper R Superscript d Baseline right-arrow double-struck upper R Superscript d of bounded mean oscillation (BMO) and theJohn–Nirenberg inequality. Here, is as usual a -dimensional volume which in this section we write as ...

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Publisher Resources

ISBN: 9781394196777Purchase Link