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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 ! I don't know, but
after I saw that replacing diff'tion by finite diff. ( like
T(f) (x) = f(x+1) - f(x) ) doesn't work, my guess is no.
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