Reputation
637
Top tag
Next privilege 1,000 Rep.
Create new tags
Badges
3 15
Newest
 Yearling
Impact
~7k people reached

Nov
9
accepted Are these critical points minima to the variational problem?
Nov
9
comment Are these critical points minima to the variational problem?
I agree with your first point...I subconsciously had considered equivalence upto multiplicative constant. In your working I think there should be the factor of half as in \begin{equation}I[tu_0]=\frac{1}{2}\int_{\Omega}-t^2u_0\triangle u_0-5\pi^2t^2u_0^2\ \mathrm{d}x\mathrm{d}y=\cdots=-\frac{3}{2}\pi^2t^2\int_{\Omega}u_0^2\ \mathrm{d}x\mathrm{d}y.\end{equation} So since there are $u_0\in\mathcal{A}$ with $I[u_0]<0$ it implies that $u$ and $v$ are not minima...correct?
Nov
9
asked Are these critical points minima to the variational problem?
Aug
24
awarded  Yearling
Aug
9
accepted Can every 2 form be represented as a linear combination of these specific two forms?
Aug
9
comment Can every 2 form be represented as a linear combination of these specific two forms?
Ah, I see so the question is asking given any 2 form $\omega$ if there exists a basis, $\mathcal{B}$, from all possible choices of bases in $V^{\ast}$ such that $(1)$ is satisfied with respect to the basis $\mathcal{B}$. Thanks this helps heaps.
Aug
8
asked Can every 2 form be represented as a linear combination of these specific two forms?
Sep
30
awarded  Explainer
Aug
24
awarded  Yearling
Jul
18
revised Real Hardy space question
added a second attempt
Jul
15
comment Hardy Space Cancellation Condition
@ Guillermo - I also don't follow the mean value theorem line; if $x_b/t$ lies in the line segment between the points $x/t$ and $(y+b_0)/t$, then shouldn't the RHS be something like \begin{equation}\frac{1}{t^{n+1}}(y+b_0-x)\cdot\phi'(x_b/t)?\end{equation}
Jul
15
revised Real Hardy space question
updated my attempt
Jul
14
comment Hardy Space Cancellation Condition
@ Guillermo - I don't understand why we integrate over $y+B$, shouldn't we be integrating over $B(y, t)$ and is $b_0\in\mathbb{R}^n$ chosen so that $|y+b_0|\geq t$?
Jul
12
comment Hardy Space Cancellation Condition
@ Guillermo - what is $b_0$?
Jul
10
revised Constructing a specific normalised test function.
edited tags
Jul
10
asked Real Hardy space question
Jul
5
comment Constructing a specific normalised test function.
Yes, I thought of rescaling $\phi$ but then while $\|D\psi\|_{\infty}\leq 1$ I don't have that $\psi$ is a normalised test function.
Jul
4
comment Constructing a specific normalised test function.
@Voliar- as in normalised test functions must integrate over $\mathbb{R^n}$ to equal 1.
Jul
4
comment Constructing a specific normalised test function.
@Voliar I was using a positive test function $\phi$ in my work.
Jul
4
revised Constructing a specific normalised test function.
added 26 characters in body