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linear_representation_of_functions [2013/09/16 10:44] nikolaj |
linear_representation_of_functions [2014/03/21 11:11] |
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| - | ===== Linearization representation ===== | ||
| - | ==== Theorem ==== | ||
| - | | $X,Y$ ... Banach spaces with topology | | ||
| - | | $f\in C(X,Y)$ | | ||
| - | | @#55EE55: $ 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 $ ^ | ||
| - | === Reference === | ||
| - | ==== Parents ==== | ||
| - | === Requirements === | ||
| - | [[Fréchet derivative]], [[Function integral]] | ||
