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Aug
15
comment Is this expression for the Riemann Tensor correct?
The c's and the p's are smooth functions on the manifold
Aug
14
comment What does this notation means in noncommutative case
But in the page en.wikipedia.org/wiki/Covariant_derivative#Formal_definition they use the notation $V f$ also to indicate the directional derivative of a function along $V$. Then it is misleading to choose one or the other alternative above. How should I interprete?
Feb
2
comment Find all the functions which satisfy a given functional equation
@DejanGovc I was editing while I received your post. Please check it again
Feb
2
comment Find all the functions which satisfy a given functional equation
@Alex did you assume $f(0)=0$ in your solution? Because then I'm pretty sure that $f(0)=-1$ is also possible. My apologies since I inverted $x,y$ in the first term of the equation. Please check the edited version. Still my apologies. BTW in this case setting $x=y=0$ gives $f(f(0))=f(0)^2+f(f(0))+f(0)$ from which $f(0)\in \{-1,0\}$.
Nov
5
comment Ordering of two weak star limits
lol you are right...
Oct
29
comment At most three different eigenvalues
@GerryMyerson I'm following the language introduced in the Birkhoff Rota Ordinary differential equation book and you can define the operator $L[u]=u'+q(x)u$ so for $\lambda$ to be an eigenvalue it means that $L[u]=\lambda u$ has a non trivial solution $u$.
Oct
29
comment At most three different eigenvalues
@JuliánAguirre it is $u'$, it is a first order DE
Oct
29
comment airy equation vanish infinitely many times
nice. Didn't know about this one. Can we solve the exercise without using that theorem?
Sep
5
comment Weak closedness implies closed and convex
how do you prove that, with your choice of $A$, $S_p(A)$ is weakly closed in $L^p(I,\mathbb R^n)$?
Aug
29
comment convergence in $L^r(I)$
$\|f_n\|_p$ is bounded
Aug
24
comment necessary conditions to be relatively compact
what if $F_\varepsilon\cap A$ is empty?
Aug
22
comment differential system on the torus
So i presume you would like to conclude that $\tilde u$ and $\tilde v$ are identically zero, being harmonic and with $0$ integral. Am I right? but unfortunately i cannot conclude by myself. Can you help me?
Aug
21
comment Estimate on the interval of definition as parameter varies
I'm afraid your calculations are not correct..
Aug
4
comment Prove that the solution tends to $0$ as $t$ goes to infinity
Excellent.. thank you did..
Aug
4
comment Prove that the solution tends to $0$ as $t$ goes to infinity
I don't get your point about symmetry.. can you please provide more details?
Aug
4
comment Prove that the solution tends to $0$ as $t$ goes to infinity
I don't know.. form your proof $<0$ seems to suffice indeed.. i copied the text as i found it..
Aug
4
comment Prove that the solution tends to $0$ as $t$ goes to infinity
Where did you used that the matrix is simmetric? Was it just a redundant information?
Jul
21
comment Prove that this function is measurable
Can you please provide more details in the first point of your argument? Still I cannot follow you completely even though you are convincing me you are right... Moreover, I can't see what is $j$ in the formula.. Of course later i will accept your answer.. Thank you Davide
Jun
11
comment $A$ has measure $0$
you mean... $\sin(n_kx)\to\pm\frac{1}{\sqrt2}$?
Jun
11
comment $A$ has measure $0$
but what if, for example, $n_k=4k+1$ and $x=\frac\pi2$? In this case the limit exists and it is constantly $1$ so I cannot claim that if the limit exists then it is $0$. I don't get your point sorry...