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 twice a superfunction MphLee Fellow Posts: 95 Threads: 7 Joined: May 2013 03/25/2014, 08:51 AM (This post was last modified: 03/25/2014, 01:00 PM by MphLee.) (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 $A=h^{\circ s}$ $B=h^{\circ t}$ and $A\circ B=B \circ A$ the functions commute but their superfunction ($H$) should be defined with $H(x+s) = A(H(x))$ $H(x+t) = B(H(x))$ then we have $h(x)=H(1+H^{-1}(x))$. But if we don't know such $s$, $t$ and $h$ and we only know that A and B commute how can we know that $f$ exist? $f(x+1) = A(f(x))$ $f(x+i) = B(f(x))$ 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 « Next Oldest | Next Newest »

 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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