Timeline for Conditions for positivity of Fourier transform
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 16, 2015 at 21:25 | comment | added | Igor Rivin | @scouser think inverse fourier transform. FT is positive -> YOUR FUNCTION is p.d. | |
| Jan 16, 2015 at 21:13 | comment | added | scouser | maybe I expressed myself incorrect in the comment. My point is that if I treat $f$ as the density of my measure, then the theorem states that $\hat{f}(p)$ is positive definite, but this does not imply that $\hat{f}(p)\geq 0$ pointwise. This is what I meant by non-negative in the question. | |
| Jan 16, 2015 at 21:04 | comment | added | Igor Rivin | @scouser what does that have to do with anything? Your function is positive by assumption, and pos. def. since the fourier transform is positive. | |
| Jan 16, 2015 at 20:59 | comment | added | scouser | Yeah, but the fact that a function is positive definite does not imply it is pointwise positive, doesn't it? | |
| Jan 16, 2015 at 20:43 | history | answered | Igor Rivin | CC BY-SA 3.0 |