7,828 reputation
31359
bio website icmat.es/giuseppe.negro
location Italy
age
visits member for 3 years, 9 months
seen 2 hours ago

PhD student, interested in PDEs of dispersive type.


1d
comment Family bounded in $\mathcal{L}^1$ has limit a.e.
The answer is no. (Keyword: Oscillation)
2d
revised Equality of two operators
added 57 characters in body
2d
comment Equality of two operators
@MikeMiller: Oh, I didn't ever notice this. Interesting. I'll leave this answer on with a warning sign, for reference.
2d
answered Equality of two operators
2d
comment Equality of two operators
This is false as it stands. You need to require symmetry of your operators.
Dec
19
awarded  Constituent
Dec
18
comment Proposed proof for convergence in Sobolev space
@JohnDoe: I know that the result is true, what I mean is that it was not properly justified. You need the Stampacchia's version of the chain rule (i.e. the one wisher mentions) to do that.
Dec
18
revised Every invertible linear transformation can be perturbed a bit without destroying invertbility, Neumann series
corrected a minor mistake in the series for (I+T)^{-1}
Dec
17
comment Proposed proof for convergence in Sobolev space
@LucioD: Of course, but it is not clear that $T_ku$ is differentiable at almost all points.
Dec
17
comment Proposed proof for convergence in Sobolev space
You should give a better justification for the inequality $$\left\lvert \frac{\partial T_k u}{\partial x_i}\right\rvert\le \left\lvert\frac{\partial u}{\partial x_i}\right\rvert.$$This is true (up to a set of measure zero), but I am not so sure it is obvious.
Dec
12
comment Verification and presentation of anisotropic sobolev space results
It seems to me that the proofs of the corresponding properties for the isotropic Sobolev spaces work verbatim for the anisotropic ones.
Dec
10
comment If $2i$ is an eigenvalue of $A_{2\times 2} \in \mathbb{R}^{2\times 2}$, find $A^2$
@Carley: Compute $D^2$ explicitly.
Dec
10
answered If $2i$ is an eigenvalue of $A_{2\times 2} \in \mathbb{R}^{2\times 2}$, find $A^2$
Dec
10
comment Why is the derivative of $x^2$ not $2x+1$?
I disagree with the downvote. Of course there is an error in the given reasoning, but the question is precisely to spot this error. Moreover, the question "shows research and effort", surely is "clear" and probably it might be also "useful" for someone studying the basics of differential calculus. IMHO, it deserves to be upvoted.
Dec
9
comment Showing $f(x) = 0$ for all $x$
Hint: Fix a generic point $x\in[a,b]$ and try to show that $f(x)=0$ by considering intervals of the form $[x-\delta, x+\delta]$. What happens when $\delta>0$ gets very small?
Dec
9
comment Express recurrence in closed form
"Closed form" is an analytical expression for the generic term of your sequence, that allows you to compute it without knowing the previous terms. In this case, $F(n)=31\cdot 5^n - 3/4$ is a closed form.
Dec
8
comment Why does it imply from that, that $f=0$ almost everywhere?
Related.
Dec
8
comment Why cannot a densely defined operator be extended to an everywhere defined operator?
To use a quantum mechanical language, I would say that such extensions are unphysical.
Dec
8
revised Why cannot a densely defined operator be extended to an everywhere defined operator?
added 105 characters in body
Dec
8
answered Why cannot a densely defined operator be extended to an everywhere defined operator?