A Basis for V2
The Haar vector space V2 has dimension 4.  One basis for V is B  = {f, y, y1,0,y1,1}.  Based on a suggestion by Prof. David Hill of Temple University, here are the graphs of these four functions, along with a table of their inner products.
 
 

The Haar father wavelet f

 

The Haar mother wavelet y

 

The Haar daughter wavelet y1,0

 



 

The Haar daughter wavelet y1,1


 
 

Table of inner products

 
f
y
y1,0
y1,1
f
1
0
0
0
y
0
1
0
0
y1,0
0
0
0.5
0
y1,1
0
0
0
0.5

 

Can you create a similar web page for B3, the wavelet basis for V3?

Web page by Edward Aboufadel, October 2000.