This directory is not really part of the
program that I am including for public use.
In particular, it has almost no documentation.
The directory contains a program I wrote for fun,
to investigate positive combinations of the functions

G_k(x)= (4-x^2)^k

of the form

F=a0 G_0 + a1 G_{e1} + ... + a4 G_{e4}

where the exponents range from 0 to 7 and
are controlled by sliders.  The exponents
need not be integers for this program.
I wanted to see if I can do better than the
maximum cutoff s=6 in the Main Theorem by
taking other linear combinations.

There are 3 main windows to this program.

1. The control panel lets you choose the
exponents e1,e2,e3,e4 and also the exponent s
of the Riesz power law.

2. One of the windows plots the difference

R_s(x) - F(x)

From x = 1.3 to x=2.  
You can see that before x=1.3, the behavior is 
obvious.   You want this to be a positive function.

3. Another window plots the values of the coefficients
you get, as s ranges from -2 to 8.  

In the two plot windows, you can change the y-coordinate
scale by factors of 2 by clicking on the rows of squares.