Timeline for On a monotonicity property of Fourier coefficients of truncated power functions
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 28, 2020 at 14:16 | comment | added | Iosif Pinelis | @JoeSilverman : Thank you for your comment. This seems to be another way to get the explicit expression for $a_{k,n}$ given in my answer. The main difficulty dealing with that expression (or in any other way with $a_{k,n}$) is that $a_{k,n}$ is oscillatory in real $n>0$. | |
| Dec 27, 2020 at 18:56 | vote | accept | Iosif Pinelis | ||
| Dec 27, 2020 at 1:30 | comment | added | Joe Silverman | Just a thought, I haven't tried to see if it leads anywhere, but what happens if you write $x^k$ as a linear combination of the Bernoulli polynomials $B_i(x)$ for $0\le i\le k$. The $n$th Fourier coefficient of the $B_i(x)$ is some (positive) multiple of $n^{-i}$. | |
| Dec 26, 2020 at 18:22 | answer | added | fedja | timeline score: 8 | |
| Dec 26, 2020 at 8:58 | comment | added | fedja | Yes, they strictly decrease for every $k>1$ (not necessarily an integer). Now it is a bit too late here for posting but I'll do it in the morning. The trick is an appropriate contour integration, as usual ;-) | |
| Dec 25, 2020 at 20:54 | answer | added | Iosif Pinelis | timeline score: 1 | |
| Dec 25, 2020 at 15:27 | history | asked | Iosif Pinelis | CC BY-SA 4.0 |