Timeline for integral depending on a parameter
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 1, 2017 at 2:35 | comment | added | CooLee | Corbennick and Michael Rendardy, Thank you very much. | |
| Jun 1, 2017 at 2:34 | vote | accept | CooLee | ||
| Jun 1, 2017 at 1:46 | answer | added | T. Amdeberhan | timeline score: 0 | |
| Jun 1, 2017 at 0:56 | comment | added | Christian Remling | The power of $s$ is irrelevant, only the exponential type matters. See my answer below please. | |
| Jun 1, 2017 at 0:55 | answer | added | Christian Remling | timeline score: 4 | |
| May 31, 2017 at 21:13 | comment | added | Michael Renardy | You can use Phragmen-Lindelof to show that the estimate actually holds for complex s. | |
| May 31, 2017 at 10:45 | comment | added | user1688 | Sorry, I thought the estimate was meant to hold for complex $s$ with $|s|>1$. | |
| May 31, 2017 at 10:35 | comment | added | Piero D'Ancona | $\sin s$ is an entire function which is bounded by $s$ | |
| May 31, 2017 at 9:46 | comment | added | CooLee | I renewed my question. | |
| May 31, 2017 at 9:46 | history | edited | CooLee | CC BY-SA 3.0 |
added 10 characters in body
|
| May 31, 2017 at 9:45 | comment | added | CooLee | Thank you very much for you hint. According to your comments, it seems that $f$ must vanish in $[0,1]$ if the power of $s$ on the right-hand side of the estimate is $\frac12$, am I right? | |
| May 31, 2017 at 9:34 | history | edited | YCor |
edited tags; edited tags
|
|
| May 31, 2017 at 9:08 | comment | added | user1688 | The integral is an entire function in $s$, so the inequality means that its Power series coefficients are zero from the second on. This is equivalent to $f$ being orthogonal to $x^k$ for $k=2,3,\dots$. | |
| May 31, 2017 at 8:24 | comment | added | user_1789 | Since the terms of order $\leq 1$ in $s$ automaticallly satisfy the inequality, one finds by expanding in $s$ that the inequality is equivalent to $|\int_0^1f(t) (e^{st}-1-st)/s^2 dt|\leq C/s$ for all $s>1$. | |
| May 31, 2017 at 6:43 | history | edited | CooLee | CC BY-SA 3.0 |
deleted 6 characters in body
|
| S May 31, 2017 at 6:29 | history | suggested | Glorfindel | CC BY-SA 3.0 |
thanks removed as per https://meta.stackexchange.com/q/2950/295232
|
| May 31, 2017 at 6:10 | review | Suggested edits | |||
| S May 31, 2017 at 6:29 | |||||
| May 31, 2017 at 5:54 | history | edited | CooLee | CC BY-SA 3.0 |
added 13 characters in body
|
| May 31, 2017 at 5:26 | history | asked | CooLee | CC BY-SA 3.0 |