Exercise 9.37. Use Theorem 9.36 to show that if ƒ € L²(R) is orthogonal to all Haar functions, then f must be zero in L²(R). D
Exercise 9.37. Use Theorem 9.36 to show that if ƒ € L²(R) is orthogonal to all Haar functions, then f must be zero in L²(R). D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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PLEASE SOLVE FOR 9.37
Transcribed Image Text:Exercise 9.37. Use Theorem 9.36 to show that if f = L²(R) is
orthogonal to all Haar functions, then f must be zero in L²(R). ◊
Theorem 9.36. For f
(9.12)
lim
M→-∞
(9.13)
L² (R), we have
||PM||2
f
= 0
lim ||PNf-f2
N→∞
= 0.
and
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