Timeline for Is $\int_{-c}^c |A \cap (x + A)|\, dx$ maximized when the measurable subset $A \subseteq \mathbb R$ is an interval centered at the origin?
Current License: CC BY-SA 4.0
10 events
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| Feb 10, 2022 at 13:05 | answer | added | dohmatob | timeline score: 2 | |
| Feb 9, 2022 at 21:54 | comment | added | dohmatob | @TerryTao Indeed, thanks for the references. Very useful. | |
| Feb 9, 2022 at 19:32 | comment | added | Terry Tao | @dohmatob Feel free to give an answer to this question to close it off. Incidentally you may be interested in some recent work on questions of this type in arxiv.org/abs/2106.13873 and arxiv.org/abs/1903.08731 . | |
| Feb 9, 2022 at 9:04 | comment | added | dohmatob | @IosifPinelis Sorry for the typos. Fixed. | |
| Feb 9, 2022 at 9:03 | comment | added | dohmatob | @TerryTao Indeed, this solves the problem. Thanks. | |
| Feb 9, 2022 at 2:05 | comment | added | Terry Tao | This is immediate from the Riesz rearrangement inequality, since $I(A) = \int_{\bf R} \int_{\bf R} 1_A(x) 1_A(x-y) 1_{[-c,c]}(y)\ dx dy$. en.wikipedia.org/wiki/Riesz_rearrangement_inequality | |
| Feb 9, 2022 at 1:11 | history | edited | dohmatob | CC BY-SA 4.0 |
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| Feb 9, 2022 at 1:06 | comment | added | Iosif Pinelis | (i) "a nonempty measurable subsets"? (ii) "respectively"? (iii) "centered at the origin"? $I(A)$ is shift-invariant. (iv) The answer at mathoverflow.net/a/282941/78539 is to a substantially different question. (v) Is your $c$ fixed? (vi) Overall, are you sure this is the question you really wanted to ask? | |
| Feb 8, 2022 at 23:31 | history | edited | dohmatob | CC BY-SA 4.0 |
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| Feb 8, 2022 at 23:25 | history | asked | dohmatob | CC BY-SA 4.0 |