Timeline for When is $\sum_{n\in\mathbb Z} f(x+n)$ constant?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 11, 2019 at 19:44 | comment | added | YCor | @u136536 if you read entirely the question, you would see that your $f$ is a particular case of a more general observation by the OP. | |
| Mar 11, 2019 at 18:35 | comment | added | u136536 | @YemonChoi: As I understand $f(x)$ may not be necessarily analytic everywhere. However, many thanks for showing this issue! | |
| Mar 11, 2019 at 18:29 | comment | added | Yemon Choi | Thank you, but my interpretation of the OP's original question is that he or she wants $f$ to be analytic everywhere. Note that sinc is analytic at the origin (removable singularity) | |
| Mar 11, 2019 at 18:25 | comment | added | u136536 | @YemonChoi: It was an error. I replaced $f(x) = \text{rect}(x)$ by $f(x) = \text{rect}(x/2)$. The function $f(x) = \text{rect}(x/2)$ is analytic within $x\in[0,1)$. | |
| Mar 11, 2019 at 18:18 | history | edited | u136536 | CC BY-SA 4.0 |
rect(x) is replaced by rect(x/2).
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| Mar 11, 2019 at 16:55 | comment | added | Yemon Choi | Perhaps I am unaware of the definition you are using. I am using this definition en.wikipedia.org/wiki/Analytic_function and your example is not analytic in this sense at $x= \pm 1/2$ since it is not continuous on any neighbourhood of these points | |
| Mar 11, 2019 at 7:28 | comment | added | Yemon Choi | The OP is asking for analytic functions satisfying the given identity | |
| Mar 11, 2019 at 5:16 | history | answered | u136536 | CC BY-SA 4.0 |