I thought 'derivation' was restricted to linear operators. Perhaps these operators should be called something like quasi-derivation, or pseudo-derivation? On 6/17/07, Dan Asimov <dasimov@earthlink.net> wrote:
Marc wrote:
<< Is there term for when f(a b) = a f(b) + b f(a)?
And the answer, supplied by Neil, is "derivation".
Okay, sure, if say C^oo(R) is the set of infinitely differentiable functions from R to R, then D: C^oo(R) -> C^oo(R) defined by
D(f)(x) = f'(x)
is perhaps the epitome of a derivation. --------------------------------------------------------------------
But what are the continuous derivations d: R -> R ?
I.e., for all real u,v, we must have
d(uv) = d(u)*v + u*d(v)
The 0 function works. What is the general solution?
--Dan
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