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Linearization representation
Theorem
$X,Y$ … Banach spaces with topology |
$f\in C(X,Y)$ |
$ f(x+y) = f(x) + \int_0^1\ Df(x+t\ y)\cdot y\ \mathrm d t $ |
Discussion
$ f(x) = f(0) + \int_0^1\ Df(t\ x)\cdot x\ \mathrm d t $ |
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