- #1
azdang
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Homework Statement
Consider the map F: C0([a,b],Rn) --> R, F([tex]\phi[/tex])=[tex]\int\phi(t)\phi(t)[/tex]dt (This is the integral from a to b). Write F as a composition of three maps, each of which is linear or bilinear. Then use the chain rule and generalized product rule to compute DF([tex]\phi[/tex]).
Homework Equations
The Attempt at a Solution
The only maps I could think of would be something like this:
[tex]\phi[/tex]: [a,b] --> Rn
A: C0([a,b],Rn) --> C0([a,b],Rn)
And then maybe I would need a map for [tex]\phi[/tex][tex]\phi[/tex]? But I'm not sure what that would be or if that's even correct. I'm not even sure that I am on the right track at all with the maps. Does anyone have any ideas?
Is it possible that F is one of the three maps? So that the composition becomes F of A of phi?