Timeline for $L^\infty-L^1$ norm of an oscillatory integral operator
Current License: CC BY-SA 4.0
6 events
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| Sep 2, 2023 at 15:35 | comment | added | Terry Tao | Oscillation of the form $e^{i( \phi(x) + \psi(y)}$ ( which your example morally has the form of) does not actually influence operator norms no matter how rapidly oscillating as it can be absorbed into the input or output function. One needs genuinely bilinear phases to get cancellation (which occurs for instance in higher dimensions in which yoyr integral is essentially a Bochner-Riesz operator). | |
| Sep 2, 2023 at 10:46 | comment | added | Fedor Petrov | Consider the characteristic function $f$ of the set of $x$ for which $\cos \lambda x>0.99$. Then $\langle T_\lambda f, f\rangle$ seems to be of order $1/\lambda$ | |
| Sep 2, 2023 at 10:00 | history | edited | capitalone | CC BY-SA 4.0 |
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| Sep 2, 2023 at 10:00 | history | edited | capitalone | CC BY-SA 4.0 |
added 26 characters in body; edited title
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| S Sep 2, 2023 at 9:48 | review | First questions | |||
| Sep 2, 2023 at 12:11 | |||||
| S Sep 2, 2023 at 9:48 | history | asked | capitalone | CC BY-SA 4.0 |