Dimension 
Decomposition 
I 1 
□ O A O 
Figure 3: Scalar products in L 2 and l 2 
Figure 1: Uniform decompositions 
(f ,x) 
linear functional 
f(x) 
Example 6 (f) 
(<T, f ) = J « (x) f(x)dx 
= f(0) 
scalar product 
<f ,x> 
Example , 
<x,y> =j' x(t)y(t)dt 
Figure 2: Bilinear form 
<a,b> 
Li^ K i 2<0 ° 
dx < 00 
representation 
general 
special 
FOURIER