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twice a superfunction
#4
(08/11/2010, 04:28 PM)tommy1729 Wrote: i have been thinking about the following often :

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))
Then the A and B always commute. I think that this is the criterion.

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
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Messages In This Thread
twice a superfunction - by tommy1729 - 08/11/2010, 04:28 PM
RE: twice a superfunction - by MphLee - 03/24/2014, 09:12 PM
RE: twice a superfunction - by tommy1729 - 03/25/2014, 12:34 AM
RE: twice a superfunction - by MphLee - 03/25/2014, 08:51 AM
RE: twice a superfunction - by tommy1729 - 03/26/2014, 01:23 PM
RE: twice a superfunction - by MphLee - 03/26/2014, 03:34 PM

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