Timeline for When is $\sum_{n\in\mathbb Z} f(x+n)$ constant?
Current License: CC BY-SA 4.0
13 events
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| Mar 11, 2019 at 15:26 | comment | added | YCor | To complete the answer to the question, it is easy to see that the family $(f_a)_{a>0}$, where $f_a(x)=\frac{2(ac\cos(ax)-\sin(ax)}{\pi x^3}$, spans a vector space of dimension $2^{\aleph_0}$ over $\mathbf{R}$, and hence the dimension of the considered vector space is $2^{\aleph_0}$. | |
| Mar 7, 2019 at 7:32 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Mar 7, 2019 at 4:46 | comment | added | reuns | If $f$ is $L^1$ then the necessary and sufficient condition is that $F(k) = 0$ for every $k \ne 0$ | |
| Mar 7, 2019 at 1:00 | comment | added | Alexandre Eremenko | I wonder why the previous question on the same subject was removed, while this one is accepted so enthusiastically:-) | |
| Mar 6, 2019 at 23:31 | comment | added | T. Amdeberhan | @Carlo: Do you need to avoid $a=1$? | |
| Mar 6, 2019 at 21:38 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Mar 6, 2019 at 20:22 | vote | accept | W-t-P | ||
| Mar 6, 2019 at 20:17 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Mar 6, 2019 at 20:15 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Mar 6, 2019 at 20:09 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Mar 6, 2019 at 20:08 | comment | added | Loïc Teyssier | @ChristianRemling: yes, I realized that ;) | |
| Mar 6, 2019 at 20:05 | comment | added | Christian Remling | @LoïcTeyssier: Yes, the original function (Dirichlet kernel) is an example. But the Poisson summation formula comes with assumptions of course, and it would be good to state explicitly what else $f$ needs to satisfy for this to work. | |
| Mar 6, 2019 at 19:56 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |