Question

Why is $f(t) = e^{ta}$ differentiable in a unital Banach algebra?

score 424 · Answer 1 · 2020-07-09 14:34:54

424

Views

Why is $f(t) = e^{ta}$ differentiable in a unital Banach algebra?

Published on 09 Jul 2020 - 14:34

score 56 · Answer 2 · 2026-03-25 15:42:24

56

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Is the inverse of an interior chart of a submanifold an immersion?

Published on 25 Mar 2026 - 15:42

score 121 · Answer 3 · 2020-07-12 10:12:23

121

Views

Graphical intuition behind general Taylor formula

Published on 12 Jul 2020 - 10:12

score 118 · Answer 4 · 2026-03-25 20:33:43

118

Views

Do diffeomorphisms between arbitrary sets extend to ordinary diffeomorphisms between open sets?

Published on 25 Mar 2026 - 20:33

score 132 · Answer 5 · 2020-07-18 19:17:02

132

Views

Can we change the order of differentiation here?

Published on 18 Jul 2020 - 19:17

score 110 · Answer 6 · 2020-07-22 12:48:22

110

Views

Frechet derivative limit

Published on 22 Jul 2020 - 12:48

score 75 · Answer 7 · 2026-03-25 20:35:42

75

Views

Are we allowed to apply the chain rule here?

Published on 25 Mar 2026 - 20:35

score 42 · Answer 8 · 2020-07-27 17:38:05

42

Views

Ambiguous definition of $f\in C^\alpha(M)$ if $M$ is a non-open submanifold

Published on 27 Jul 2020 - 17:38

score 65 · Answer 9 · 2016-08-22 14:27:08

65

Views

Error Bound for Fréchet Differentiable Functionals

Published on 22 Aug 2016 - 14:27

score 48 · Answer 10 · 2016-08-28 09:27:43

48

Views

Fréchet derivative of $x\mapsto{\rm D}A(x)\circ B(x)$ with $A:H\to H$ and $B:H\to\mathfrak L(U,H)$

Published on 28 Aug 2016 - 9:27

score 40 · Answer 11 · 2016-09-10 21:49:47

40

Views

If $u\in C^{1,\:2}([0,T]\times\Omega,\mathbb R^d)$, what can we say about the Fréchet differentiability of $t\mapsto u(t,\;\cdot\;)$?

Published on 10 Sep 2016 - 21:49

score 138 · Answer 12 · 2016-11-23 11:45:46

138

Views

How to find out the frechet derivative of the following non linear function?

Published on 23 Nov 2016 - 11:45

score 38 · Answer 13 · 2016-11-24 19:32:09

38

Views

Prove that a series, containing the Fréchet derivative of a function, converges in a Hilbert space

Published on 24 Nov 2016 - 19:32

score 198 · Answer 14 · 2016-11-30 15:49:17

198

Views

Limit definition of second derivative in vector spaces

Published on 30 Nov 2016 - 15:49

score 103 · Answer 15 · 2016-12-01 14:49:20

103

Views

If $G\in C^2(H,\mathfrak L(U,H))$, what's the Fréchet derivative of $\Phi(x)(u,v):=({\rm D}G(x)(G(x)u))v$?

Published on 01 Dec 2016 - 14:49

List Question

Why is $f(t) = e^{ta}$ differentiable in a unital Banach algebra?

Is the inverse of an interior chart of a submanifold an immersion?

Graphical intuition behind general Taylor formula

Do diffeomorphisms between arbitrary sets extend to ordinary diffeomorphisms between open sets?

Can we change the order of differentiation here?

Frechet derivative limit

Are we allowed to apply the chain rule here?

Ambiguous definition of $f\in C^\alpha(M)$ if $M$ is a non-open submanifold

Error Bound for Fréchet Differentiable Functionals

Fréchet derivative of $x\mapsto{\rm D}A(x)\circ B(x)$ with $A:H\to H$ and $B:H\to\mathfrak L(U,H)$

If $u\in C^{1,\:2}([0,T]\times\Omega,\mathbb R^d)$, what can we say about the Fréchet differentiability of $t\mapsto u(t,\;\cdot\;)$?

How to find out the frechet derivative of the following non linear function?

Prove that a series, containing the Fréchet derivative of a function, converges in a Hilbert space

Limit definition of second derivative in vector spaces

If $G\in C^2(H,\mathfrak L(U,H))$, what's the Fréchet derivative of $\Phi(x)(u,v):=({\rm D}G(x)(G(x)u))v$?

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