Question
This task can be applied to bounded operators using the Riesz-Thorin theorem. For 10 points each:
[10m] Name this task that involves creating new data within the range of an existing dataset.
ANSWER: interpolation
[10e] The Riesz-Thorin theorem implies that the Hausdorff-Young inequality holds for this operation. This operation applied to f equals the integral over the real numbers with respect to t of (read slowly) f of t times the exponential of minus 2 pi i x t.
ANSWER: Fourier transform [do not accept "Fourier series"]
[10h] The Hausdorff-Young inequality is proved by interpolating between the space of square integrable functions and functions with this property almost everywhere. L infinity is the set of functions that have this property almost everywhere.
ANSWER: boundedness
<Andrew Rout , Science - Other - Math Pure>
Summary
| 2023 NASAT | 06/17/2023 | Y | 8 | 12.50 | 75% | 50% | 0% |
Data
| Asia B | Kentucky B | 0 | 10 | 0 | 10 |
| California | Liberia | 10 | 10 | 0 | 20 |
| Illinois Orange | Kentucky A | 10 | 10 | 0 | 20 |
| Illinois White | Virginia | 0 | 10 | 0 | 10 |
| Maryland Gold | Missouri A | 10 | 10 | 0 | 20 |
| Maryland Red | New Jersey B | 10 | 10 | 0 | 20 |
| New Jersey A | Ohio | 0 | 0 | 0 | 0 |
| Missouri B | Pennsylvania | 0 | 0 | 0 | 0 |