Nirav
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 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 $$I[tu_0]=\frac{1}{2}\int_{\Omega}-t^2u_0\triangle u_0-5\pi^2t^2u_0^2\ \mathrm{d}x\mathrm{d}y=\cdots=-\frac{3}{2}\pi^2t^2\int_{\Omega}u_0^2\ \mathrm{d}x\mathrm{d}y.$$ 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 $$\frac{1}{t^{n+1}}(y+b_0-x)\cdot\phi'(x_b/t)?$$ 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