Timeline for (Dis)continuity of periodic functions with non-summable Fourier series
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 1, 2020 at 15:10 | comment | added | Goulifet | I see, the comparison with the continuous case is effectively interesting. | |
| Jun 1, 2020 at 15:08 | comment | added | Christian Remling | The perturbation in my comment refers to $d_n$, if you write $c_n=|n|^{-\alpha}+d_n$. | |
| Jun 1, 2020 at 14:20 | comment | added | Goulifet | I am not sure to understand: what is the perturbation you are talking about? Do you know if there is anything like the result $\mathcal{F} \{ \lvert t \rvert^{-\alpha} \}(x) = c \lVert x \rvert^{\alpha - d}$ for the periodic setting? (I realized there was a mistake in the context for the parameter $\alpha$, I corrected it.) | |
| Jun 1, 2020 at 14:17 | history | edited | Goulifet | CC BY-SA 4.0 |
mistake correction
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| Jun 1, 2020 at 14:14 | comment | added | Christian Remling | At least in the context situation, this sounds right, since at least in the continuous case $|t|^{-\alpha}$ has FT $c|x|^{\alpha -d}$, and the perturbation has a smooth FT, so won't affect the behavior at $x=0$. | |
| May 31, 2020 at 23:10 | history | edited | Goulifet | CC BY-SA 4.0 |
Update of the hypotheses on c_n(f)
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| May 31, 2020 at 22:48 | history | asked | Goulifet | CC BY-SA 4.0 |