User contributions for FvomEnde

29 December 2022

• 08:4808:48, 29 December 2022 diff hist −9‎ Derivative of Product of Operator-Valued Functions ‎No edit summary Tags: Reverted Visual edit: Switched

9 December 2022

• 11:5311:53, 9 December 2022 diff hist −169‎ Differentiable Operator-Valued Function is Continuous ‎No edit summary
• 11:4611:46, 9 December 2022 diff hist +15‎ Differentiable Operator-Valued Function is Continuous ‎No edit summary
• 11:4411:44, 9 December 2022 diff hist +258‎ Differentiable Operator-Valued Function is Continuous ‎No edit summary
• 11:4111:41, 9 December 2022 diff hist −904‎ Derivative of Product of Operator-Valued Functions ‎No edit summary
• 11:3611:36, 9 December 2022 diff hist +2,448‎ N 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..."

7 December 2022

• 19:3019:30, 7 December 2022 diff hist +4‎ m Definition:Differentiable Mapping/Function With Values in Normed Space ‎No edit summary current
• 13:2213:22, 7 December 2022 diff hist −51‎ Derivative of Product of Operator-Valued Functions ‎ fixed typo
• 11:5911:59, 7 December 2022 diff hist +132‎ Derivative of Product of Operator-Valued Functions ‎ Added more steps where {{explain}} was inserted
• 11:4911:49, 7 December 2022 diff hist +3‎ Derivative of Product of Operator-Valued Functions ‎ typo
• 11:4811:48, 7 December 2022 diff hist +198‎ Derivative of Product of Operator-Valued Functions ‎ Put inequalities where they should be & added extra step between line 3 & 4 in first calclucation
• 09:1609:16, 7 December 2022 diff hist +247‎ Derivative of Product of Operator-Valued Functions ‎ Added reference which features the result in question (albeit without proof)
• 09:1209:12, 7 December 2022 diff hist −228‎ Definition:Derivative/Function With Values in Normed Space ‎ Changed reference from a book on Fréchet differentiability to a book which actually treats infinite-dimensional vector valued functions
• 09:1209:12, 7 December 2022 diff hist −206‎ Definition:Differentiable Mapping/Function With Values in Normed Space ‎ Changed reference from a book on Fréchet differentiability to a book which actually treats infinite-dimensional vector valued functions

6 December 2022

• 12:1312:13, 6 December 2022 diff hist −96‎ Derivative of Product of Operator-Valued Functions ‎No edit summary
• 12:1312:13, 6 December 2022 diff hist +53‎ Talk:Derivative of Product of Operator-Valued Functions ‎No edit summary current

5 December 2022

• 21:3121:31, 5 December 2022 diff hist +270‎ Definition:Derivative/Function With Values in Normed Space ‎No edit summary
• 21:2921:29, 5 December 2022 diff hist −202‎ Definition:Differentiable Mapping/Function With Values in Normed Space ‎No edit summary
• 14:3314:33, 5 December 2022 diff hist +277‎ N 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)"
• 14:1914:19, 5 December 2022 diff hist −8‎ Definition:Derivative/Function With Values in Normed Space ‎No edit summary
• 14:1914:19, 5 December 2022 diff hist +449‎ Derivative of Product of Operator-Valued Functions ‎No edit summary
• 14:1414:14, 5 December 2022 diff hist +93‎ Definition:Differentiable Mapping/Function With Values in Normed Space ‎No edit summary
• 14:1014:10, 5 December 2022 diff hist +173‎ Definition:Derivative ‎No edit summary
• 14:0914:09, 5 December 2022 diff hist +821‎ N 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..."

4 December 2022

• 13:0213:02, 4 December 2022 diff hist +57‎ Product Rule for Derivatives ‎No edit summary
• 13:0213:02, 4 December 2022 diff hist +3,774‎ N 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(..."
• 12:2212:22, 4 December 2022 diff hist −5‎ Definition:Differentiable Mapping/Function With Values in Normed Space ‎No edit summary
• 12:1312:13, 4 December 2022 diff hist +397‎ N 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)"
• 12:0712:07, 4 December 2022 diff hist −54‎ Derivative of Product of Real Function and Vector-Valued Function ‎No edit summary current
• 12:0512:05, 4 December 2022 diff hist −26‎ Derivative of Product of Real Function and Vector-Valued Function ‎ Proof correct Tag: Visual edit
• 12:0312:03, 4 December 2022 diff hist −10‎ Definition:Differentiable Mapping/Function With Values in Normed Space ‎No edit summary
• 12:0312:03, 4 December 2022 diff hist −44‎ Definition:Differentiable Mapping/Function With Values in Normed Space ‎No edit summary
• 11:5211:52, 4 December 2022 diff hist +14‎ Definition:Differentiable Mapping ‎No edit summary
• 11:5111:51, 4 December 2022 diff hist +183‎ Definition:Differentiable Mapping ‎No edit summary
• 11:4911:49, 4 December 2022 diff hist +680‎ N 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 February 2021

• 14:3814:38, 15 February 2021 diff hist +1‎ Separable Space satisfies Countable Chain Condition ‎ Fixed typo current
• 14:0614:06, 15 February 2021 diff hist +733‎ Separable Space satisfies Countable Chain Condition ‎ Added missing proof

2 February 2021

• 08:0808:08, 2 February 2021 diff hist +3‎ Continuous Composition of Measurable Functions into Second Countable Space is Measurable ‎ Sigma isn't necessarily the countable union of measurable sets (indeed for every measurable A, sigma = A U (sigma/A), but there's not much of a point to this decomposition), rather the point is that Sigma *contains* such countable unions. Also \RR is mathcal R, but the reals are denoted by mathbb R (which is \R) current

1 February 2021

• 17:1617:16, 1 February 2021 diff hist +387‎ User talk:FvomEnde ‎No edit summary
• 15:1415:14, 1 February 2021 diff hist +20‎ Continuous Composition of Measurable Functions into Second Countable Space is Measurable ‎No edit summary
• 15:1215:12, 1 February 2021 diff hist +3,902‎ N 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..."

7 December 2020

• 07:4407:44, 7 December 2020 diff hist +78‎ User:FvomEnde ‎No edit summary current
• 07:4407:44, 7 December 2020 diff hist +60‎ User:FvomEnde ‎No edit summary