Timeline for When are Fourier coefficients monotonic?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 6, 2021 at 18:15 | comment | added | Yemon Choi | Can I just point out that this definition of "Fourier coefficient" looks a bit strange for $f(x)=\sin(x)$, which last time I looked was a perfectly reasonable $2\pi$-periodic smooth function... | |
| Jan 6, 2021 at 11:55 | comment | added | Yemon Choi | Are you only interested in even functions $f$, i.e. those satisfying $f(x)=f(2\pi -x)$? If not then your definition of "Fourier coefficient" might not be appropriate | |
| Dec 28, 2020 at 16:44 | vote | accept | spaceman | ||
| Dec 28, 2020 at 14:30 | history | edited | YCor | CC BY-SA 4.0 |
fixed typo, changed tag
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| Dec 26, 2020 at 19:11 | answer | added | Salcio | timeline score: 3 | |
| Dec 25, 2020 at 9:23 | history | became hot network question | |||
| Dec 25, 2020 at 3:48 | answer | added | Iosif Pinelis | timeline score: 25 | |
| Dec 24, 2020 at 19:41 | comment | added | Fedor Petrov | @Itay but it's higher derivatives are quite large in a sense. | |
| Dec 24, 2020 at 19:40 | comment | added | spaceman | Hi @Itay, I'm not necessarily looking for a smoothness condition, but just another general condition for this to hold, e.g. a sufficient decay, has to satisfy condition (X) etc. type of condition. The smoothness assumption was put in place to simplify matters. | |
| Dec 24, 2020 at 19:11 | comment | added | Itay | I doubt there will be such a condition in terms of smoothness. Given any smooth function $f$ and a positive integer $n$, the function $f- \hat{f}(n) cos(nx)$ has the same Fourier coefficients as $f$, besides the $n$th, which would be 0. | |
| Dec 24, 2020 at 18:15 | history | asked | spaceman | CC BY-SA 4.0 |