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8/14 Let 1 < p < 0. For t = [0, 1], let xi(t) = 1, -{ 1, if 0 ≤t≤ 1/2 -1, if 1/2

8/14 Let 1 < p < 0. For t = [0, 1], let xi(t) = 1, -{ 1, if 0 ≤t≤ 1/2 -1, if 1/2

Advanced Engineering Mathematics
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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8/14 Let 1 < p <∞. For t = [0, 1], let x1(t) = 1, -{ 1, if 0 ≤t≤ 1/2 -1, if 1/2 <t≤1 and for n = 1,2,..., j = 1,...,2", Ign+j(t) = { T₂(t) = 2n/p, if (2j-2)/2n+1 ≤t≤ (2j-1)/2n+1 -2n/P, if (2j-1)/2n+1 <t≤2j/2n+1 otherwise. 0, Then the Haar system (x1, x2, 3,...) is a Schauder basis for LP([0, 1]). Each an is a step function.
Transcribed Image Text:8/14 Let 1 < p <∞. For t = [0, 1], let x1(t) = 1, -{ 1, if 0 ≤t≤ 1/2 -1, if 1/2 <t≤1 and for n = 1,2,..., j = 1,...,2", Ign+j(t) = { T₂(t) = 2n/p, if (2j-2)/2n+1 ≤t≤ (2j-1)/2n+1 -2n/P, if (2j-1)/2n+1 <t≤2j/2n+1 otherwise. 0, Then the Haar system (x1, x2, 3,...) is a Schauder basis for LP([0, 1]). Each an is a step function.
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