(3) Consider the function defined as : R -> R>0 if laT 1 2 p(x) 0 if a> np(nx), and let Kn(x) be the restriction of pn to the For all integers n > 1, define pn(x) := interval (, . Verify that {Kn(x)}n>1 is an approximation to the identity

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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(3) Consider the function
defined as
: R -> R>0
if laT
1
2
p(x)
0 if a>
np(nx), and let Kn(x) be the restriction of pn to the
For all integers n > 1, define pn(x) :=
interval (, . Verify that {Kn(x)}n>1 is an approximation to the identity
Transcribed Image Text:(3) Consider the function defined as : R -> R>0 if laT 1 2 p(x) 0 if a> np(nx), and let Kn(x) be the restriction of pn to the For all integers n > 1, define pn(x) := interval (, . Verify that {Kn(x)}n>1 is an approximation to the identity
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