Timeline for Bounding the discrete $l^p$ norm by the continuous $L^p$ norm for trigonometric polynomials
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 4, 2022 at 4:09 | vote | accept | Chushamm | ||
| Nov 3, 2022 at 16:56 | comment | added | Terry Tao | As long as the points sampled are separated from each other by at least a constant multiple of the natural spatial uncertainty (in this case, $1/N$), one obtains an upper bound of this form (one can think of this as a manifestation of the uncertainty principle). The lower bound is more interesting (one needs the sampling points to be at least as dense as the Shannon sampling threshold) and becomes quite delicate if the sampling points are not equally spaced (deep theorems such as Beurling-Malliavin become relevant). | |
| Nov 3, 2022 at 5:33 | comment | added | Chushamm | Thanks. I'm also confused about how the validity of the result depends on the discrete points selected. Is the set of points that guarantees the equality of l^2 norm and L^2 norm the only possible choice or is it not that essential? | |
| Nov 2, 2022 at 19:00 | history | answered | Terry Tao | CC BY-SA 4.0 |