|
|
Ulysse from CH wrote:
> On 29 Sep 2006 17:59:13 -0700, theronruiz@xxxxxxxxxxx wrote:
>
> >S is the set of all R -> R functions.
> >T is a S -> S function such that:
> >T(f o g) = (T(f) o g) * T(g) for every f and g in S,
> >where (f o g)(x) = f(g(x)) and (f * g)(x) = f(x) * g(x).
> >Are there non-constant solutions?
> >
> If you replace S by C_oo(R;R) differentiation
> is a solution ! Probably this does not come as a surprise
> to you and you want to know if a non-c. solution exists
> that works for all functions R->R !
Maybe this is an illogical dream.
I would like to know, whether it is possible to exist non-trivial
function T: S -> S, such that:
T(f o g) = W(T(f), T(g), f, g) for every f and g in S,
where W is a S^4 -> S map.
In other words: is it possible to exist some function that decomposes
the composition operator o: S^2 -> S, as described above?
Thank you,
Theron
|
|