7,345 reputation
31153
bio website icmat.es/giuseppe.negro
location Spain
age
visits member for 3 years, 5 months
seen 8 hours ago

PhD student, interested in PDEs of dispersive type.


9h
reviewed Close Ellipse representation when Directrix and focus given
9h
reviewed Close Allyson replaced 100
9h
reviewed Leave Open How to find intelligently counterexamples for (dis)proofs about matrices?
9h
reviewed Close topology problem read
9h
reviewed Leave Open Linear Transformation $T-T^2=I$
Aug
20
awarded  Socratic
Aug
9
comment Extension of function with values in a Banach space
The line that you are trying to prove (i.e. $\|y+re\|\le 1\Rightarrow \|y\|\le M$) amounts to the proof that the projection of $E$ onto $Y$ along the vector $e$ is a continuous linear operator.
Aug
6
reviewed Close Structure theorem of modules in the graded case
Aug
6
comment Rellich's theorem for Sobolev space on the torus
Think at a toy model with $k_1=0$ first. It should be easier.
Aug
6
comment Rellich's theorem for Sobolev space on the torus
There is a remark (Remark 2) on this blog entry of Terence Tao: terrytao.wordpress.com/2008/11/05/… that says something vaguely related to your problem. (Vaguely here means very vaguely)
Aug
6
comment Rellich's theorem for Sobolev space on the torus
I think that the idea is the following. Taking $N$ to be big, you are activating more Fourier modes while you are still requiring that the weighted sum of their squares be $1$. So the total "mass" of $1$ spreads out on more modes. In the lower-regularity space, modes have a smaller weight applied on them, and so this spreading results in a lowering of the norm.
Aug
6
comment Proof of rank-nullity via the first isomorphism theorem
Related to my previous comment: math.stackexchange.com/q/752056/8157
Aug
6
comment Proof of rank-nullity via the first isomorphism theorem
Not only this works, it is more natural from an algebraic point of view. Moreover, it gives a version of the theorem that applies to infinite-dimensional vector spaces as well (i.e. the first isomorphism theorem). I am a fan of this approach.
Aug
6
comment Can a non-constant two dimensional polynomial have a set of zero points of positive measure?
Try $f(x, y)=x^2+y^2-1$
Aug
6
reviewed Edit suggested edit on Finding an inverse laplace transform for $\displaystyle\frac{a}{\left(s^2 + a^2\right)^2}$
Aug
6
revised Finding an inverse laplace transform for $\displaystyle\frac{a}{\left(s^2 + a^2\right)^2}$
improved formatting
Aug
6
reviewed Approve suggested edit on Slots Machine Matching feature
Aug
6
reviewed Approve suggested edit on Evaluate the $\displaystyle\lim_{x\to 0}\left(\frac{1}{x\sqrt{1+x}}-\frac 1x\right)$
Aug
5
comment Exchange the order of the two limits
Hasty answer: this holds whether one of the limits exists uniformly with respect to the other variable. This is explained well on Lang's textbook Undergraduate analysis.
Aug
5
revised Ways to calculate the spectrum of an operator
added 36 characters in body