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 Tumbleweed
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Aug
30
answered Find the critical point and show it is not a global minimizer (using Hessian)
Aug
29
awarded  Tumbleweed
Aug
22
asked Principal value with truncation in $y$-direction
Aug
22
comment Decomposition of measures acting on sobolev spaces
@NormalHuman: The $H^{-1}$ norm is not local, thus measures with disjoint support may not be orthogonal. Moreover, it is not clear why this strategy would fail in 1 dimensions. I think I managed to construct a counterexample in dimension 2, but I need to check it again.
Aug
20
answered Is there a text introducing “high order Fréchet derivative” well?
Aug
20
comment Is there a text introducing “high order Fréchet derivative” well?
Since you are satisfied, I will post it as an answer.
Aug
20
comment Is there a text introducing “high order Fréchet derivative” well?
A nice textbook which introduces higher order Fréchet derivatives is "Differential Calculus" by Cartan.
Aug
19
asked Decomposition of measures acting on sobolev spaces
Aug
19
awarded  Self-Learner
Aug
14
revised Decomposition of functionals on sobolev spaces
added 172 characters in body
Aug
14
revised Decomposition of functionals on sobolev spaces
added 21 characters in body
Aug
13
comment Proof that $\lim_{n\to\infty}\|x_n-x\|=0$ with weak convergence
Thank you for this nice paper. Just for reference: The counterexample is the following: Take $X = (\mathbb{R^2}, \|\cdot\|_{\ell^1})$. Then, $L^2(0,1;X)$ is a counterexample.
Aug
13
comment Why $T+3I$ or $T-3I$ is isomorphism if $T : \mathbb{R}^3 \rightarrow \mathbb{R}^3 $ is linear with $\dim\ker T =2$.
Can you express the eigenvalues of $T - 3 \, I$ in terms of the eigenvalues of $T$?
Aug
10
comment do you know any example which is not lattice norm?
You can find it, e.g., in Schaefer's "Banach Lattices and Positive Operators", p.5, (8).
Aug
9
comment How do i convince students in high school for which this equation: $2^x=4x$ have only one solution in integers that is $x=4$?
There is another root between $0$ and $1$, see wolframalpha.com/input/?i=2^x-4=0.
Aug
8
answered Show that function is in L^2
Aug
6
comment Big an open ball inside small open ball in metric space
But with your metric, you have $B(1/2, 1/4) = B(1/2,1/5) = \{1/2\}$.
Aug
5
comment Big an open ball inside small open ball in metric space
What are the three values $1, 1/2, 1/4$ resp. $2, 1/2, 1/5$ of your balls?
Aug
5
comment Big an open ball inside small open ball in metric space
No, your intervals aren't balls. In particular, $d(1/2, 1) = 3/2$ and $d(1/2,1/2+1/5) = 9/5 > 3/2$. Hence, each ball around $1/2$ which contains $1/2 + 1/5$ will also contain $1$.
Aug
4
comment Big an open ball inside small open ball in metric space
And at which point and for which radius?