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Combined display of all available logs of ProofWiki. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).
- 11:36, 9 December 2022 FvomEnde talk contribs created page Differentiable Operator-Valued Function is Continuous (Created page with "== Theorem == Let $\struct {X, \norm \cdot_X}$ and $\struct {Y, \norm \cdot_Y}$ normed vector spaces. Let $\map B {X, Y}$ denote the space of bounded linear transformations between $X$ and $Y$. Let $f : I \to \map B {X, Y}$ be a map defined on an interval $I$ whose image are Defini...")
- 14:33, 5 December 2022 FvomEnde talk contribs created page Talk:Derivative of Product of Operator-Valued Functions (Created page with "Added definition of $B(X,Y)$ etc. & I linked the definition of the derivative of vector-valued functions wherever appropriate--FvomEnde (talk) 14:33, 5 December 2022 (UTC)")
- 14:09, 5 December 2022 FvomEnde talk contribs created page Definition:Derivative/Function With Values in Normed Space (Created page with "== Definition == <onlyinclude> Let $U \subset \R$ be an open set. Let $\struct {X, \norm {\, \cdot \,}_X}$ be a normed vector space. Let $f : U \to X$ be differentiable at $x \in U$. The '''derivative of $\mathbf f$ at $x$''' is defined as the element $\map {f'} x \in X$ which satisfies :$\ds \lim_{h \mathop \to 0} \nor...")
- 13:02, 4 December 2022 FvomEnde talk contribs created page Derivative of Product of Operator-Valued Functions (Created page with "== Theorem == <onlyinclude> Let $\struct {X, \norm \cdot_X}$, $\struct {Y, \norm \cdot_Y}$, and $\struct {Z, \norm \cdot_Z}$ normed vector spaces. Let $A : \R \to B(X,Y)$ and $B : \R \to B(Y,Z)$ differentiable functions with values in the bounded linear transformations. The product $AB : \R \to B(X,Z)$, $x \mapsto A(...")
- 12:13, 4 December 2022 FvomEnde talk contribs created page Definition talk:Differentiable Mapping/Function With Values in Normed Space (Created page with "Good point, I wasn't sure whether to turn this into the general Fréchet derivative and call it "Functions Between Normed Spaces" or that would be "too much of an upgrade" of the current page; hence why I settled for real domains first. But I'll gladly change this to functions between arbitrary normed spaces --FvomEnde (talk) 12:13, 4 December 2022 (UTC)")
- 11:49, 4 December 2022 FvomEnde talk contribs created page Definition:Differentiable Mapping/Function With Values in Normed Space (Created page with "== Definition == <onlyinclude> Let $U \subset \R$ be an open set. Let $\struct {X, \norm \cdot_X}$ be a normed vector space. A function $f : U \to X$ is '''differentiable''' at $x \in U$ {{iff}} there exists $f'(x) \in X$ such that: :$\ds \lim_{h \mathop \to 0} \Big\|\frac {\map f {x+h} - \map f {x}} h-f'(x)\Big\|_{X}=0$ </onlyinclude> == Sources == * {{BookReference|Foundations of Modern Ana...")
- 15:12, 1 February 2021 FvomEnde talk contribs created page Continuous Composition of Measurable Functions into Second Countable Space is Measurable (Created page with "== Theorem == Let $\tuple {X, \Sigma}$ be a measurable space. Let $\tuple {X_i, \tau_i}$ for $i=1,\ldots,n$ and $\tuple {Y, \tau_Y}$ be Def...")