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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]] |