(08/11/2010, 04:28 PM)tommy1729 Wrote: i have been thinking about the following often :Then the A and B always commute. I think that this is the criterion.

how and when is a function a 'superfunction for two functions' and what degrees of freedom do we have ?

for instance

assume the following equation

f(x+1) = A(f(x))

f(x+i) = B(f(x))

But maybe the the fact that they commute is too general maybe.

example

and

the functions commute but their superfunction () should be defined with

then we have .

But if we don't know such , and and we only know that A and B commute how can we know that exist?

By the way I don't think that we can define a new superfunction from two functions A and B when they don't commute... if it is possible is really weird and interesting...

Have you found some example where we dont need that they commute and the superfunction exist?

PS: I replied to your private message.

MathStackExchange account:MphLee