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linear_representation_of_functions [2013/09/15 21:49] nikolaj created |
linear_representation_of_functions [2014/03/21 11:11] (current) |
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| ===== Linearization representation ===== | ===== Linearization representation ===== | ||
| ==== Theorem ==== | ==== Theorem ==== | ||
| - | | @#88DDEE: $X,Y$ ... Banach spaces with topology | | + | | $X,Y$ ... Banach spaces with topology | |
| - | | @#88DDEE: $f\in C(X,Y)$ | | + | | $f\in C(X,Y)$ | |
| - | | @#55EE55: $ f(x+y) = f(x) + \int_0^1\ Df(x+t\ y)\cdot y\ \mathrm d t $ | | + | | @#55EE55: postulate | @#55EE55: $ f(x+y) = f(x) + \int_0^1\ Df(x+t\ y)\cdot y\ \mathrm d t $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
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| === Reference === | === Reference === | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Fréchet derivative]], [[Function integral]] | [[Fréchet derivative]], [[Function integral]] | ||
