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Jul
2
awarded  Curious
Jun
23
awarded  Organizer
Jun
23
comment An inequality between integrals of series of characteristic functions of cubes
There was a very similar question answered here: math.stackexchange.com/questions/807426/… I would like to know if one could do this for $p<1$
Jun
23
revised An inequality between integrals of series of characteristic functions of cubes
harmonic analysis is more appropriate here than just "analysis"
Jun
23
suggested suggested edit on An inequality between integrals of series of characteristic functions of cubes
May
15
answered An analysis qual problem
Apr
11
awarded  Yearling
Mar
16
comment Prove that the Laplacian of the integral of a certain function is $0$
This is essentially the Poisson extension: en.wikipedia.org/wiki/Poisson_kernel
Mar
16
comment Prove that the Laplacian of the integral of a certain function is $0$
Are you missing a $y$ on the numerator?
Feb
16
comment For what values of $p>0, \quad \int^{1}_{0} \frac{x}{\sin{(x^{p})}} \operatorname d\!x$ converges?
There isn't any oscillation near $0$ to prevent the integral to blowing up as you make $t$ apporach $0$. So my guess is that this exists whenever $0< p <2$ and diverges for all $p \geq 2$. That this blows up for $p\geq 2$ can easily be proved using the estimate $\sin(x) \leq x$. That it converges for $0<p<2$ can be shown using the estimate $\sin(x) \geq 2x/\pi$ (for $0\leq x \leq \pi/2$).
Feb
10
comment How to find $\int_{S^2}f \cdot n \ \text{d}S$ if $f(x,y,z):=(x^3,y^3,z^3)^T$
You can easily integrate $g(x,y,z)=3x^2+3y^2+3z^2$ over the ball by using spherical coordinates together with the fact that $g$ is invariant under rotations. You will get something in terms of the surface area of the sphere.
Feb
7
revised Measure of sections - continuous?
deleted 6 characters in body
Feb
7
comment Measure of sections - continuous?
It's constant in $(a,b)$ of course, but not globally.
Feb
7
answered Measure of sections - continuous?
Feb
7
comment Measure of sections - continuous?
$f$ is not constant, it's piece-wise constant.
Feb
7
comment Measure of sections - continuous?
Note that this fails to address the counterxample for non-homeomorphic sections Ofir is talking about.
Feb
4
comment Analogue of Lebesgue differentiation theorem in Orlicz spaces
You mean your right-hand sides to be $|f(x)|$?
Jan
31
comment Showing that the Lebesgue measure is “continuous”
Maybe approximating will work. The example I had in mind was something like $E = \{\frac{1}{2^k}:\, k \in \mathbb{N}\}$. It seems like $E \cap (E+\frac{1}{n})$ is oscillating between the empty set and a couple of numbers.
Jan
31
comment Showing that the Lebesgue measure is “continuous”
Actually, the other inclusions are not true in general either.
Jan
29
comment How to calculate this complex integral: $\int_0^{2\pi}\cot(t-ia)dt$, where $a>0$.
Can you show your work?