Timeline for Convolution with the Jacobi Theta-function on "both the space and time variables" - still jointly smooth?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 19, 2023 at 0:26 | vote | accept | Isaac | ||
| Jul 18, 2023 at 23:10 | comment | added | Iosif Pinelis | @Isaac : This seems to be a more difficult question, which you may want to post separately. | |
| Jul 18, 2023 at 22:20 | comment | added | Isaac | Or does the above convolution operation improve regularity of $f$ by at least order $1$? That is, $\Theta *f$ is at least jointly continuous in $(x,t)$ and continuously differentiable with respect to $x$ under my conditions? | |
| Jul 18, 2023 at 21:54 | comment | added | Iosif Pinelis | @Isaac : I think that, at a minimum, you need to require $f(\cdot,t)$ to be the restriction to $[0,1]$ of a smooth $1$-periodic function. | |
| Jul 18, 2023 at 21:38 | comment | added | Isaac | Thank you again for your detailed answer. Perhaps, could you give me insight on what would be a regularity condition on $f(x,t)$ with respect to $x$ that ensures the convolution to be smooth with respect to $x$? | |
| Jul 18, 2023 at 21:05 | comment | added | Iosif Pinelis | @Isaac : Please see the added detail. | |
| Jul 18, 2023 at 21:04 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 53 characters in body
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| Jul 18, 2023 at 20:56 | comment | added | Isaac | Thank you. How about smoothness in $x$ only? | |
| Jul 18, 2023 at 20:52 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |