Let f = C(R/Z; C), and for n= 0,1,2,... define 2/₁₁ (2) cos(2x)da; by = 2(a) sin(2xnx)da. 0,1] Show that the series 1 40+(a, cos(2nz)+b, sin(2xnx)) n-1 converges in L²-metric to f.
Let f = C(R/Z; C), and for n= 0,1,2,... define 2/₁₁ (2) cos(2x)da; by = 2(a) sin(2xnx)da. 0,1] Show that the series 1 40+(a, cos(2nz)+b, sin(2xnx)) n-1 converges in L²-metric to f.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.5: Applications
Problem 17EQ
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Transcribed Image Text:1. Let f = C(R/Z; C), and for n=0,1,2,... define
2/₁1 (2) cos(2+12)da; b = 2√(2) sin(2xnx)da.
a=2
Show that the series
1
00+ Σ(a, cos(272) + b₁ sin(2xnx))
n-1
converges in L2-metric to f.
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