Timeline for The maximal difference between a function and translates of itself
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 20, 2023 at 2:05 | comment | added | Iosif Pinelis | @GiorgioMetafune : Thank you for your comment, which finalizes the matter. | |
| Aug 19, 2023 at 15:57 | comment | added | Giorgio Metafune | The best constant is 1. This is seen best for measures: just take a $\delta$ at any point. For any $t$, the total variation of the difference between $\delta$ and $\delta_t$ is 2 as well as that of $\delta-1$. For functions, one approximates the $\delta$ with $\epsilon^{-1} \chi (0, \epsilon)$. | |
| Aug 18, 2023 at 1:52 | comment | added | Nate River | Oh.. so it is haha | |
| Aug 18, 2023 at 1:52 | comment | added | mathworker21 | @NateRiver It's the triangle inequality for integrals: $$\int_{S^1} \left| f(x) - \int_{S^1} f(x+t)dt \right| dx \le \int_{S^1} \int_{S^1} |f(x)-f(x+t)| dt dx.$$ | |
| Aug 18, 2023 at 1:39 | comment | added | Iosif Pinelis | @mathworker21 : This is a good question. I don't think that $C=1$ is optimal. Do you have an idea about the optimal value? | |
| Aug 18, 2023 at 1:38 | vote | accept | Nate River | ||
| Aug 18, 2023 at 1:33 | comment | added | mathworker21 | $+1$, is $C=1$ optimal? | |
| Aug 18, 2023 at 1:32 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 54 characters in body
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| Aug 18, 2023 at 1:26 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |