Timeline for Derivative bounds for self convolution of the spherical measure in $R^d$
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 22 at 10:08 | comment | added | Zygmund | @IosifPinelis yes. It is. I have added that in the question. | |
| Nov 22 at 10:07 | history | edited | Zygmund | CC BY-SA 4.0 |
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| Nov 21 at 12:54 | comment | added | Iosif Pinelis | Is $\chi$ smooth? | |
| Nov 21 at 2:42 | comment | added | Zygmund | @IosifPinelis. I believe one can show that $\tilde{\sigma} \ast \sigma$ is absolutely continuous with respect to the Lebesgue measure, and we are talking about its Radon--Nikodym derivative. | |
| Nov 21 at 2:33 | comment | added | Zygmund | @AlekseiKulikov, sorry about the confusion. $d\theta$ is the standard spherical measure on $\mathbb{S}^{d-1}$. The purpose of $\chi$ is to localise the measure. If it is supported on a ball centered at the north pole with radius $\leq 1/2$, then we can see that $\sigma$ is supported on the half sphere. Does this clarify your doubt? | |
| Nov 19 at 13:02 | comment | added | Iosif Pinelis | What is the meaning of $\partial^{\gamma} (\widetilde{\sigma} \ast \sigma)(x)$, given that $\widetilde{\sigma} \ast \sigma$ is a measure? | |
| Nov 19 at 7:46 | comment | added | Aleksei Kulikov | To be honest, now I am even more confused, as I do not seem to understand what is $\sigma$ (you say it is a measure on a sphere, but then talk about a function $\chi$ with a support in a ball of radius $\frac{1}{2}$). | |
| Nov 19 at 6:04 | comment | added | Zygmund | @AlekseiKulikov, I have edited the question to include the definitions. | |
| Nov 19 at 6:03 | history | edited | Zygmund | CC BY-SA 4.0 |
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| Nov 19 at 5:50 | comment | added | Aleksei Kulikov | Could you please explain what do you mean by a reflection of a measure? | |
| Nov 19 at 5:42 | history | edited | Zygmund |
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| S Nov 19 at 5:31 | review | First questions | |||
| Nov 19 at 6:46 | |||||
| S Nov 19 at 5:31 | history | asked | Zygmund | CC BY-SA 4.0 |