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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

6 The Proof of Theorem 2.3

In this chapter we will establish Theorem 2.3 and hence immediately Theorem 2.2 follows [39].

6.1 Proof of Theorem 2.3 (part(2))

We begin with the proof of Theorem 2.3 (part(2)).

Proof: We argue by way of contradiction that the result does not hold. Then for each l greater-than-or-equal-to 1, we can find points y 1 Superscript left-parenthesis l right-parenthesis Baseline comma ellipsis comma y Subscript k Superscript left-parenthesis l right-parenthesis and z 1 Superscript left-parenthesis l right-parenthesis Baseline comma ellipsis comma z Subscript k Superscript left-parenthesis l right-parenthesis in double-struck upper R Superscript d satisfying (2.3) with delta equals 1 slash l but not satisfying (2.4). Without loss of generality, we may suppose that diam StartSet y 1 Superscript left-parenthesis l right-parenthesis Baseline comma ellipsis comma y Subscript k Superscript left-parenthesis l right-parenthesis Baseline EndSet equals 1 for each l and that y 1 Superscript left-parenthesis l right-parenthesis Baseline equals 0 and z Subscript l Superscript left-parenthesis 1 right-parenthesis Baseline equals 0 for each l. Thus for all and and

for and any ...

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Publisher Resources

ISBN: 9781394196777Purchase Link