# Tag Info

### On a Poincaré inequality with weight

Such an inequality cannot exist. Take $\Omega=B_1(0)\subset \mathbb{R}^n$ and assume find a constant $C>0$ independent of $\omega$, then taking a sequence $(w_k)_k \subset L^p(B_1)$ weakly ...
Accepted

### $L^1$ error between indicator function and smoothed out version

Yes, this works, and the only ingredient we need is the estimate $\int_r^{\infty} e^{-t^2}\, dt\lesssim e^{-r^2}$. We then have (for example) \begin{align*} \int_r^{\infty} |f_r(x)|\, dx &=\frac{1}...

### Eigenfunctions of the integral kernel $1/(x^2 + x'^2)$

I think I have a solution, however I cannot reproduce your asymptotic at $x\rightarrow\infty$ (although it agrees at $x\rightarrow 0$). Also I was unable to evaluate the original integral with my ...
Accepted

### Convergence of spectrum

$C^0$-convergence is sufficinent. Note that $\lambda_i$ can be defined as the least lower bound on numbers $\lambda$ such that the following property holds: There is an $i$-dimensional subspace $W$ ...

### Relationship between noncommutative torus for different values of theta

Jamie Gabe has already pointed out why the answer is negative, but I wanted to point out that in fact the negative answer has nothing to do with Cstar algebras, quantum tori, or anything beyond the ...
Accepted

### Is the projective limit $\mathcal{D}(\mathbb{R})$ separable?

The projective topology topology you describe is coarser than the usual inductive limit topology on $\mathscr D(\mathbb R)$ (the universal properties imply that it is enough to have continuity of the ...
### Pointwise convergence and disjoint sequences in $C(K)$
I claim that either of your properties (sequences or nets) is equivalent to having only finitely many non-isolated points. Property $S$: Any pointwise null sequence in $C(K)$ has an almost disjoint ...