Reputation
341
Top tag
Next privilege 500 Rep.
Access review queues
Badges
2 13
Newest
 Investor
Impact
~3k people reached

  • 0 posts edited
  • 0 helpful flags
  • 14 votes cast
Apr
12
comment inserting absolute value in Hilbert transform and a discrete version of Hilbert transform
In the paper you mentioned, the authors only said "the discrete Hilbert transform is bounded" without giving a proof.
Mar
26
comment evaluating $\int_0^{k!}e^{i\frac{t^k}{k!}} dt$
@Dr.MV The exercise says so. You see that the upper limit of the integral and the coefficient of $x^k$ match. I suspect that there should be some nice cancellation going on.
Mar
26
awarded  Investor
Mar
25
comment evaluating $\int_0^{k!}e^{i\frac{t^k}{k!}} dt$
@Dr.MV Sorry for my late reply and thank you for your answer. I got this question from an exercise in a textbook and it seems to me the integral should depend linearly on $k$.
Mar
12
asked evaluating $\int_0^{k!}e^{i\frac{t^k}{k!}} dt$
Mar
3
comment quadratic Gauss sum over a power of 2
@Elaqqad For any $a$ and $b$?
Mar
2
asked quadratic Gauss sum over a power of 2
Feb
24
comment $\|f\|_2\le\|f\|_4^{\frac{2}{3}}\|f\|_1^{\frac{1}{3}}$
OK. So this should be a lemma for the RT interpolation theorem, not a consequence of it?
Feb
23
asked $\|f\|_2\le\|f\|_4^{\frac{2}{3}}\|f\|_1^{\frac{1}{3}}$
Feb
22
asked an inequality in Banach algebra
Feb
21
accepted construction of a curve connecting two points
Feb
21
comment construction of a curve connecting two points
I can see your idea behind the construction. But does it guarantee that $p$ is increasing?
Feb
11
comment uniform bound for sine integral function
@DavideMarano Here $a>0$. So the fact the integrand is odd is not helpful.
Feb
11
comment uniform bound for sine integral function
Did you mean $a=0, b=\pi$? The function is odd.
Feb
11
awarded  Yearling
Feb
10
asked uniform bound for sine integral function
Feb
10
asked construction of a curve connecting two points
Feb
10
asked an inequality on convolution
Feb
10
comment Is $C_c$ dense in $L_p$ for $0<p<1$?
@ PhoemueX Thank you. I just came up with another idea. I'm trying to reduce the $p<1$ case to the "p=1" case. Given $f\in L_p$, we can find a sequence of functions in $C_c^\infty$ that converges to $f^p$ in $L_1$. Then I don't how to proceed.
Feb
6
comment Is $C_c$ dense in $L_p$ for $0<p<1$?
It seems that the proof is the same as in the case $p\ge 1$. So we do not need a norm here: a quasi-norm is fine. Am I correct?